rotation free isogeometric thin shell analysis using pht splines this paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical t meshes pht splines the method exploits the flexibility of t meshes for local refinement the main advantage of the pht splines in the context of thin shell theory is that it achieves c1 continuity so the kirchhoff love theory can be used in pristine form no rotational degrees of freedom are needed numerical results show the excellent performance of the present method

robust stability analysis of linear time delay systems by lambert w function some extreme point results robust stability conditions are derived for linear time delay systems using lambert w function the characteristic quasi polynomials of the systems are assumed to be factorized it is proven that if uncertainties in the coefficients of the quasi polynomial are set in appropriate regions in the complex plane we can enjoy extreme point results finite number of stability checks at some points of the boarder of the regions suffice the strength of lambert w function approach lies in the fact that the function is implemented on some standard software packages such as mathematica maple or matlab which afford to compute the function value very easily the above two points make the stability test for the class of uncertain time delay systems quite practical

notes on big ray tracing it is well known that eikonal solvers provide a fast and accurate way to compute traveltimes in complex media however they only give solutions corresponding to first arrivals in j comput phys 128 463 1996 j d benamou presents an algorithm which gives a multivalued traveltime solution on the whole domain considered by defining subdomains in this domain in such a way that within these subdomains the traveltime is single valued and can be found by an eikonal solver restricted to the subdomain the subdomains may overlap but together they constitute the whole domain the solution on the whole domain is then given by the combination of the solutions on the subdomains an approximate realisation of these subdomains called big rays is given in the present paper we describe some problems the algorithm shows and give an explanation of their origin we conclude that the method cannot be used in the presence of caustics

linear systems with commensurate time delays stability and stabilization independent of delay notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays constructive methods for determining a stabilizing feedback are also presented the last part of the paper deals with a standard type of observer and regulator with the requirement that the closed loop system be stable independent of delay

c2 interpolation t splines abstract in this work we construct a class of c 2 interpolation t spline called it spline basis functions over regular t meshes a new rule for determining the local knot vectors of the it spline basis functions is designed the resulting it spline basis functions are always linearly independent for regular t meshes in order to guarantee the partition of unity and compact support properties of the it spline basis functions several modified schemes are developed an iteration adjustment algorithm for adjusting the points on it spline surface to the targeted points is proposed some applications of the new it spline basis functions in fitting bivariate functions and open 3d meshes solving numerical pdes and iga are given

robust hurwitz stability test for linear systems with uncertain commensurate time delays the note deals with the robust hurwitz stability of a class of linear systems with uncertain commensurate time delays which is formulated as the robust hurwitz stability of a nonpolytopic family of quasi polynomials a np hard problem from the viewpoint of computational complexity on the basis of the edge theorem and sylvester resultant elimination a necessary and sufficient condition is developed for the robust stability of the whole family and it yields an effective testing procedure an illustrative example is given to show the effectiveness of the method

parametric mesh regularization for interpolatory shape design and isogeometric analysis over a mesh of arbitrary topology abstract isogeometric analysis iga over a mesh of arbitrary topology is a challenging task since the concept of iga was proposed in the literature one can find some results in iga over an irregular mesh based on approximating schemes while little work is reported so far using interpolatory schemes this paper presents a parametric mesh regularization pmr method for iga using mapped interpolatory basis functions over a mesh of arbitrary topology given a geometric model defined over a mesh of arbitrary topology a global parametric mesh is first defined from the given control mesh using a gravity center method gcm yuan and ma 2014 the resulting parametric mesh is further regularized such that it ensures absolute interpolatory modeling with mapped interpolatory basis functions necessary geometric rules are developed for the regularization process while maintaining the same mesh topological structure the interpolatory basis function used in this paper is a kind of truncated interpolatory basic function tibf studied in our early work yuan and ma 2013 it can also be applied to other mapped interpolatory basis functions in addition to the capability of interpolatory modeling the proposed pmr method can also be applied to approximating schemes which further enriches the capability of such schemes in both modeling and isogeometric analysis of some models in a more appropriate and convenient manner the proposed pmr method has also the potential in achieving higher order continuity at extraordinary vertices using higher order mapped interpolatory basis functions

isogeometric indirect boundary element method for solving the 3d acoustic problems abstract this paper provides an isogeometric indirect boundary element method igibem based on nurbs non uniform rational b splines and pht splines polynomial splines over hierarchical t meshes for analyzing the three dimensional 3d acoustic problems in the classical procedure the geometries are discretized by lagrange polynomials elements which leads to both substantial geometrical error and time consuming meshing steps however these deficiencies can be eliminated by the isogeometric analysis iga directly incorporating the geometry description generated from the cad computer aided design software into cae computer aided engineering analysis unlike the dbem direct boundary element method the ibem indirect boundary element method allows different types of boundary conditions on the two sides of a surface moreover the hypersingular integrals in ibem can be transformed to a weakly singular form in addition the pht based ibem is used to investigate the influence of local refinement on the accuracy of solutions finally the non uniqueness problem is solved which is a fatal defect in the acoustic bem for the exterior problem four different methods to handle the non uniqueness problem are discussed and compared the results obtained by the proposed method were compared with analytical solutions and the results computed by lagrange based ibem several benchmark examples demonstrate 1 the present method i e igibem has super accuracy over conventional ibem for the acoustic problems 2 local refinement has a significant influence on the convergence rate of the solutions and the numerical accuracy is relevant to the distance to the boundary where the local refinement acted 3 as for the non uniqueness problem the imposition of specific interior boundary conditions not only obtains the best calculation result over the entire range of frequencies but also has a simple integral formulation

extended isogeometric analysis based on pht splines for crack propagation near inclusions summary adaptive local refinement is one of the main issues for isogeometric analysis iga in this paper an adaptive extended iga xiga approach based on polynomial splines over hierarchical t meshes pht splines for modeling crack propagation is presented the pht splines overcome certain limitations of non uniform rational b splines nurbs based formulations in particular they make local refinements feasible to drive the adaptive mesh refinement we present a recovery based error estimator for the proposed method the method is based on the xiga method in which discontinuous enrichment functions are added to the iga approximation and this method does not require remeshing as the cracks grow in addition crack propagation is modeled by successive linear extensions that are determined by the stress intensity factors sifs under linear elastic fracture mechanics the proposed method has been used to analyze numerical examples and the sifs results were compared with reference results the findings demonstrate the accuracy and efficiency of the proposed method this article is protected by copyright all rights reserved

a coupled iga meshfree discretization of arbitrary order of accuracy and without global geometry parameterization abstract this article presents a novel approach for coupling of isogeometric analysis iga and meshfree discretizations taking advantage of the strengths of both techniques we make iga responsible for the representation of the exact geometry of the problem domain boundary while the reproducing kernel particle method rkpm discretization is employed in the interior of the domain the coupling procedure relies on the higher order consistency or reproducing conditions that are directly imposed in the physical domain the resulting iga rkpm coupling technique preserves the geometric exactness of iga while circumventing the need for global volumetric parameterization of the problem domain and achieves arbitrary order approximation accuracy while maintaining higher order smoothness of the discretization numerical examples demonstrate the optimal convergence properties of the coupled iga rkpm formulation and show its effectiveness in constructing volumetric discretizations for complex geometry objects

linear independence of the t spline blending functions associated with some particular t meshes based on the local refinement algorithm addressed in sederberg et al 2004 17 we analyze the linear independence of the bi cubic t spline blending functions corresponding to particular t meshes

isogeometric analysis of large deformation thin shells using rht splines for multiple patch coupling we present an isogeometric thin shell formulation for multi patches based on rational splines over hierarchical t meshes rht splines nitsche s method is employed to efficiently couple the patches the rht splines have the advantages of allowing a computationally feasible local refinement are free from linear dependence possess high order continuity and satisfy the partition of unity and non negativity in addition the c1c1 continuity of the rht splines avoids the rotational degrees of freedom the good performance of the present method is demonstrated by a number of numerical examples

robust stability of perturbed systems with time delays abstract motivated by dynamical system considerations a number of new results on robust stability of perturbed polynomials have been recently obtained in the literature under consideration the perturbations are known only within given bounds and enter affine linearly into the polynomial coefficients in this paper this formulation is expanded to include time delays under a properness assumption a necessary and sufficient condition for robust stability is developed an example is given to illustrate application of the main result

locking free stabilized conforming nodal integration for meshfree mindlin reissner plate formulation abstract the cause of shear locking in mindlin reissner plate formulation is due to the inability of the numerical formulation in representing pure bending mode without producing parasitic shear deformation lack of kirchhoff mode to resolve shear locking in meshfree formulation of mindlin reissner plates the following two issues are addressed 1 construction of approximation functions capable of reproducing kirchhoff modes and 2 formulation of domain integration of galerkin weak form capable of producing exact solution under pure bending condition in this study we first identify the kirchhoff mode reproducing conditions kmrc and show that the employment of a second order monomial basis in the reproducing kernel or moving least square approximation of translational and rotational degrees of freedom is an effective means to meet kmrc next the integration constraints that fulfill bending exactness be in the galerkin meshfree discretization of mindlin reissner plate are derived a nodal integration with curvature smoothing stabilization that fulfills be is then formulated for mindlin reissner plate the curvature smoothing stabilization is introduced in the nodally integrated galerkin weak form the resulting meshfree formulation is stable and free of shear locking in the limit of thin plate both computational efficiency and accuracy are achieved in the proposed meshfree mindlin reissner plate formulation

new rotation free finite element shell triangle accurately using geometrical data a new triangle shell element is presented the advantages of this element are threefold simplicity generality and geometrical accuracy the formulation is free from rotation degrees of freedom the triangle here presented can be used regardless of the mesh topology thus generality is conserved for any mesh represented surface from an original first order approach we evolve to a third order geometric description the higher degree geometric description is based on the bezier triangles concept a very well known geometry in the domain of cagd g farin curves and surfaces for cagd a practical guide fifth ed morgan kaufmann publishers san francisco ca 2002 using this concept we show the path to reconstruct a general third order interpolating surface using only the three coordinates at each node this work takes as starting point the nodal implementation of a basic triangle shell element e onate f zarate rotation free triangular plate and shell elements int j numer methods engrg 47 2000 557 603 in order to use an exact formula for the curvature the normal directions at each node and the way to characterize them are proposed then the geometrical properties and the mechanical behavior of the surface created are introduced finally different examples are presented to depict the versatility and accuracy of the element

a nitsche type formulation and comparison of the most common domain decomposition methods in isogeometric analysis this paper provides a detailed elaboration and assessment of the most common domain decomposition methods for their application in isogeometric analysis the methods comprise a penalty approach lagrange multiplier methods and a nitsche type method for the nitsche method a new stabilized formulation is developed in the context of isogeometric analysis to guarantee coercivity all these methods are investigated on problems of linear elasticity and eigenfrequency analysis in 2d in particular focus is put on non uniform rational b spline patches which join nonconformingly along their common interface thus the application of isogeometric analysis is extended to multi patches which can have an arbitrary parametrization on the adjacent edges moreover it has been shown that the unique properties provided by isogeometric analysis that is high order functions and smoothness across the element boundaries carry over for the analysis of multiple domains copyright 2013 john wiley sons ltd

isogeometric analysis enhanced by the scaled boundary finite element method abstract by leveraging the information of a typical cad model in the analysis the intensive process of discretization can be circumvented this unification has led to the isogeometric analysis iga hughes et al 2005 however as the cad model provides information only of the boundary a 2d 3d stress analysis is still one major step away in this work the concepts of isogeometric analysis and the scaled boundary finite element method sbfem are combined the sbfem requires only the boundary information and hence provides a seamless integration with the cad modeling within the proposed framework the nurbs basis functions are used to discretize the unknown fields in the circumferential direction whilst analytical solution is sought in the radial direction we further extend the framework to problems with singularities and to dynamic analysis the accuracy and the convergence properties of the proposed method are demonstrated with benchmark problems in the context of linear elasticity and linear elastic fracture mechanics

a new rotation free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries abstract this paper presents a general non linear computational formulation for rotation free thin shells based on isogeometric finite elements it is a displacement based formulation that admits general material models the formulation allows for a wide range of constitutive laws including both shell models that are extracted from existing 3d continua using numerical integration and those that are directly formulated in 2d manifold form like the koiter canham and helfrich models further a unified approach to enforce the g 1 continuity between patches fix the angle between surface folds enforce symmetry conditions and prescribe rotational dirichlet boundary conditions is presented using penalty and lagrange multiplier methods the formulation is fully described in the natural curvilinear coordinate system of the finite element description which facilitates an efficient computational implementation it contains existing isogeometric thin shell formulations as special cases several classical numerical benchmark examples are considered to demonstrate the robustness and accuracy of the proposed formulation the presented constitutive models in particular the simple mixed koiter model that does not require any thickness integration show excellent performance even for large deformations

reissner mindlin shell implementation and energy conserving isogeometric multi patch coupling summary a shear flexible isogeometric reissner mindlin shell formulation using non uniform rational b splines basis functions is introduced which is used for the demonstration of a coupling approach for multiple non conforming patches the six degrees of freedom formulation uses the exact surface normal vectors and curvature the shell formulation is implemented in an isogeometric analysis framework for computation of structures composed of multiple geometric entities to enable local model refinement as well as non matching domains coupling a conservative multi patch approach using lagrange multipliers for structured non uniform rational b splines patches is presented here an additional border frame mesh is used to couple geometries during structural analyses this frame interface approach avoids the problem of excessive constraints when multiple patches are coupled at one point first the shell formulation is verified with several reference cases then the influence of the frame interface discretization and frame penalty stiffness on the smoothness of the results is investigated the effects of the perturbed lagrangian method in combination with the frame interface approach is shown in addition results of models with t joint interface connections and perpendicular stiffener patches are presented copyright 2016 john wiley sons ltd

isogeometric fluid structure interaction analysis with emphasis on non matching discretizations and with application to wind turbines abstract in this paper we develop a framework for fluid structure interaction fsi modeling and simulation with emphasis on isogeometric analysis iga and non matching fluid structure interface discretizations we take the augmented lagrangian approach to fsi as a point of departure here the lagrange multiplier field is defined on the fluid structure interface and is responsible for coupling of the two subsystems thus the fsi formulation does not rely on the continuity of the underlying function spaces across the fluid structure interface in order to produce the correct coupling conditions between the fluid and structural subdomains however in deriving the final fsi formulation the interface lagrange multiplier is formally eliminated and the formulation is written purely in terms of primal variables avoiding the use of lagrange multipliers adds efficiency to the proposed formulation as an added benefit the ability to employ non matching grids for multi physics simulations leads to significantly relaxed requirements that are placed on the geometry modeling and meshing tools for iga we show an application of the proposed fsi formulation to the simulation of the nrel 5 mw offshore wind turbine rotor where the aerodynamics domain is modeled using volumetric quadratic nurbs while the rotor structure is modeled using a cubic t spline based discretization of a rotation free kirchhoff love shell we conclude the article by showing fsi coupling of a t spline shell with a low order finite element method fem discretization of the aerodynamics equations this combined use of iga and fem is felt to be a good balance between speed robustness and accuracy of fsi simulations for this class of problems

a higher order stress based gradient enhanced damage model based on isogeometric analysis abstract the micro damage associated with diffuse fracture processes in quasi brittle materials can be described by continuum damage mechanics in order to overcome the mesh dependence of local damage formulations non local and gradient enhanced approaches are often employed in this manuscript a higher order stress based gradient enhanced formulation is proposed which exploits the higher order continuity of b spline functions in isogeometric analysis iga the proposed formulation does not require the decomposition of the fourth order model into two second order models two numerical examples are presented to demonstrate the performance of the formulation and to compare the obtained solutions with results from conventional gradient enhanced damage formulation

a hermite reproducing kernel approximation for thin plate analysis with sub domain stabilized conforming integration a hermite reproducing kernel rk approximation and a sub domain stabilized conforming integration ssci are proposed for solving thin plate problems in which second order differentiation is involved in the weak form although the standard rk approximation can be constructed with an arbitrary order of continuity the proposed approximation based on both deflection and rotation variables is shown to be more effective in solving plate problems by imposing the kirchhoff mode reproducing conditions on deflectional and rotational degrees of freedom simultaneously it is demonstrated that the minimum normalized support size coverage of kernel functions can be significantly reduced with this proposed approximation the galerkin meshfree framework for thin plates is then formulated and the integration constraint for bending exactness is also derived subsequently an ssci method is developed to achieve the exact pure bending solution as well as to maintain spatial stability numerical examples demonstrate that the proposed formulation offers superior convergence rates accuracy and efficiency compared with those based on higher order gauss quadrature rule copyright 2007 john wiley sons ltd

delay independent stability test for systems with multiple time delays delay independent stability dis of a general class of linear time invariant lti multiple time delay system mtds is investigated in the entire delay parameter space stability of such systems may be lost only if their spectrum lies on the imaginary axis for some delays we build an analytical approach that requires the inspection of the roots of finite number of single variable polynomials in order to detect if the spectrum ever lies on the imaginary axis for some delays excluding infinite delays the approach enables to test the necessary and sufficient conditions of dis of lti mtds technically known as weak dis as well as the robust stability of single delay systems against all variations in delay ratios the proposed approach which does not require any parameter sweeping and graphical display becomes possible by establishing a link between the infinite spectrum and algebraic geometry case studies are provided to show the effectiveness of the approach

locking free isogeometric collocation methods for spatial timoshenko rods in this work we present the application of isogeometric collocation techniques to the solution of spatial timoshenko rods the strong form equations of the problem are presented in both displacement based and mixed formulations and are discretized via nurbs based isogeometric collocation several numerical experiments are reported to test the accuracy and efficiency of the considered methods as well as their applicability to problems of practical interest in particular it is shown that mixed collocation schemes are locking free independently of the choice of the polynomial degrees for the unknown fields such an important property is also analytically proven

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

isogeometric analysis using polynomial splines over hierarchical t meshes for two dimensional elastic solids isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries one of the major drawbacks of nurbs based isogeometric finite elements is the inefficiency of local refinement in this study we present an alternative to nurbs based isogeometric analysis that allows for local refinement the idea is based on polynomial splines and exploits the flexibility of t meshes for local refinement the shape functions satisfy important properties such as non negativity local support and partition of unity several numerical examples are used to demonstrate the reliability of the present method

an iga discontinuous galerkin method on the union of overlapped patches abstract in isogeometric analysis iga the discontinuous galerkin method iga dg is often applied when the domain is composed of multiple non uniform rational b splines nurbs patches these patches are often required to be c 0 continuous to make the iga dg available and this requirement brings some problems to the cad process this paper extends the iga dg method to solve problems on the union of the overlapped patches with this method igaodg a problem on the overlapped domain is seen as multiple sub problems on the non trimmed patches and then the continuities of traces of the numerical solutions are penalized on the boundaries of non trimmed elements with the coefficients deduced from the classical dg method comparing with the iga methods which apply the cad boolean operations to deal with the overlapped domains the presented method carries out the integrations in the non trimmed patches thus no additional integration scheme needs to be considered to achieve the gaussian integration precision discussions on the presented discretization scheme and its convergence analysis show that this method is available on the domain created by the union of the matched mismatched and overlapped patches as predicted in the convergence analysis the presented method gives the optimal convergence rates in our numerical examples finally through one of its engineering applications this paper shows how to extend igaodg to solve problems that are defined on the trimmed patches

an exact method for the stability analysis of time delayed linear time invariant lti systems a general class of linear time invariant systems with time delay is studied recently they attracted considerable interest in the systems and control community the complexity arises due to the exponential type transcendental terms in their characteristic equation the transcendentality brings infinitely many characteristic roots which are cumbersome to elaborate as evident from the literature a number of methodologies have been suggested with limited ability to assess the stability in the parametric domain of time delay this study offers an exact structured and robust methodology to bring a closure to the question at hand ultimately we present a unique explicit analytical expression in terms of the system parameters which not only reveals the stability regions pockets in the domain of time delay but it also declares the number of unstable characteristic roots at any given pocket the method starts with the determination of all possible purely imaginary resonant characteristic roots for any positive time delay to achieve this a simplifying substitution is used for the transcendental terms in the characteristic equation it is proven that the number of such resonant roots for a given dynamics is finite each one of these roots is created by infinitely many time delays which are periodically distributed an interesting property is also claimed next that the root crossing directions at these locations are invariant with respect to the delay and dependent only on the crossing frequency these two unique findings facilitate a simple and practical stability method which is the highlight of the work

parameter dependent lyapunov functions for robust stability of time varying linear systems under point delays abstract this paper investigates the stabilization dependent on the delays of in general time varying linear systems with multiple constant point time delays the matrices describing the state space dynamics are parameterized by in general time varying function matrices governed by coefficient functions in compact sets the closed loop sufficiency type stability conditions are obtained from lyapunov s stability theory by constructing parameter dependent candidates which satisfy in the most general case a riccati matrix differential inequality

an isogeometric design through analysis methodology based on adaptive hierarchical refinement of nurbs immersed boundary methods and t spline cad surfaces we explore hierarchical refinement of nurbs as a basis for adaptive isogeometric and immersed boundary analysis we use the principle of b spline subdivision to derive a local refinement procedure which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions we test hierarchical refinement of nurbs for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases using the b spline version of the finite cell method we illustrate the potential of immersed boundary methods as a seamless isogeometric design through analysis procedure for complex engineering parts defined by t spline cad surfaces specifically a ship propeller and an automobile wheel we show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features

isogeometric kirchhoff love shell formulation for elasto plasticity abstract an isogeometric thin shell formulation allowing for large strain plastic deformation is presented a stress based approach is adopted which means that the constitutive equations are evaluated at different integration points through the thickness allowing the use of general 3d material models the plane stress constraint is satisfied by iteratively updating the thickness stretch at the integration points the deformation of the shell structure is completely described by the deformation of its midsurface and furthermore the formulation is rotation free which means that the discrete shell model involves only three degrees of freedom several numerical benchmark examples with comparison to fully 3d solid simulations confirm the accuracy and efficiency of the proposed formulation

shape optimization directly from cad an isogeometric boundary element approach using t splines abstract we develop a t spline isogeometric boundary element method igabem simpson et al 2012 scott et al 2013 simpson et al 2014 to shape sensitivity analysis and gradient based shape optimization in three dimensional linear elasticity contrary to finite element based isogeometric analysis iga approaches no parametrization of the volume is required hence the iterative optimization algorithm can be implemented directly from cad without any mesh generation or postprocessing step for returning the resulting structure to cad designers t splines also guarantee a water tight geometry without the manual geometrical repair work as with non uniform rational b splines nurbs we demonstrate the worth of the method by analysing problems with and without analytical solutions including engineering examples involving complex shapes additionally we provide all the derivations of the required sensitivities and the details pertaining to the geometries examined in the benchmarking to provide helpful reference problems for 3d shape optimization

a collocated c0 finite element method reduced quadrature perspective cost comparison with standard finite elements and explicit structural dynamics summary we demonstrate the potential of collocation methods for efficient higher order analysis on standard nodal finite element meshes we focus on a collocation method that is variationally consistent and geometrically flexible converges optimally embraces concepts of reduced quadrature and leads to symmetric stiffness and diagonal consistent mass matrices at the same time it minimizes the evaluation cost per quadrature point thus reducing formation and assembly effort significantly with respect to standard galerkin finite element methods we provide a detailed review of all components of the technology in the context of elastodynamics that is weighted residual formulation nodal basis functions on gauss lobatto quadrature points and symmetrization by averaging with the ultra weak formulation we quantify potential gains by comparing the computational efficiency of collocated and standard finite elements in terms of basic operation counts and timings our results show that collocation is significantly less expensive for problems dominated by the formation and assembly effort such as higher order elastostatic analysis furthermore we illustrate the potential of collocation for efficient higher order explicit dynamics throughout this work we advocate a straightforward implementation based on simple modifications of standard finite element codes we also point out the close connection to spectral element methods where many of the key ideas are already established copyright 2014 john wiley sons ltd

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

a novel three variable shear deformation plate formulation theory and isogeometric implementation abstract this study brings to readers the generalized formulation of three variable plate theory and an efficient computational approach for analyzing plates the theory not only has three degree of freedoms dofs per node which complies with three dimensional space of full plate model as classical plate theory cpt but also accounts for the effect of shear deformation without any requirement of shear correction factors scf a complete set of strong forms weak form as well as classical and non classical boundary conditions bcs for linear and geometrically nonlinear analysis are consistently derived in this paper through a variational approach the strong forms are sixth order differential equations resulting in the symmetrical fourth order differential weak form it is known that isogeometric analysis iga arguably outweighs classical finite element method in terms of high continuity and high order differentiability thanks to its advantage an iga framework for the generalized three variable plate theory is formulated with completely locking free and only three dofs per node the classical bcs are strongly enforced to system equations as usual whilst the non classical bcs are weakly imposed by a penalty approach the new plate theory with only three variable is thereafter used for static linear and nonlinear analysis of isotropic and functionally graded material fgm plates to demonstrate its ability the reliability and accuracy of the present approach are ascertained by comparing the obtained results with other existing ones based on a robust formulation devoted in the paper the proposed approach can be further extended for numerous problems related to the shear deformable effect in the literature

novel higher order mass matrices for isogeometric structural vibration analysis abstract a set of novel higher order mass matrices are presented for isogeometric analysis of structural vibrations using nurbs the proposed method for the construction of higher order mass matrices contains two essential steps firstly based upon the standard consistent mass matrix a special reduced bandwidth mass matrix is designed this reduced bandwidth mass matrix meets the requirement of mass conservation while simultaneously preserves the same order of frequency accuracy as the corresponding consistent mass matrix subsequently a mixed mass matrix is formulated through a linear combination of the reduced bandwidth mass matrix and the consistent mass matrix the desired higher order mass matrix is then deduced from the mixed mass matrix by optimizing the linear combination parameter to achieve the most favorable order of accuracy both quadratic and cubic formulations are discussed in detail and it is shown that with regard to the vibration frequency the proposed higher order mass matrices have 6th and 8th orders of accuracy in contrast to the 4th and 6th orders of accuracy associated with the quadratic and cubic consistent mass matrices a generalization to two dimensional higher order mass matrix is further realized by the tensor product operation on the one dimensional reduced bandwidth and consistent mass matrices a series of benchmark examples congruously demonstrate that the proposed higher order mass matrices are capable of achieving the theoretically derived optimal accuracy orders for structural vibration analysis

analysis of thin shells by the element free galerkin method a meshless approach to the analysis of arbitrary kirchhoff shells by the element free galerkin efg method is presented the shell theory used is geometrically exact and can be applied to deep shells the method is based on moving least squares approximant the method is meshless which means that the discretization is independent of the geometric subdivision into finite elements the satisfaction of the c1 continuity requirements is easily met by efg since it requires only c1 weights therefore it is not necessary to resort to mindlin reissner theory or to devices such as discrete kirchhoff theory the requirements of consistency are met by the use of a polynomial basis of quadratic or higher order a subdivision similar to finite elements is used to provide a background mesh for numerical integration the essential boundary conditions are enforced by lagrange multipliers membrane locking which is due to different approximation order for transverse and membrane displacements is removed by using larger domains of influence with the quadratic basis and by using quartic polynomial basis which can prevent membrane locking completely it is shown on the obstacle course for shells that the present technique performs well

isogeometric symmetric galerkin boundary element method for three dimensional elasticity problems abstract the isogeometric analysis iga is applied for the weakly singular symmetric galerkin boundary element method sgbem to analyzelinear elastostatics problems in three dimensional domains the background of the proposed method is to use non uniform rational b splines nurbs as the basis functions for the approximation of both geometry and field variables i e displacement and traction of the governing integral equations same as weakly singular sgbem the basic ingredient of the method is a pair of weakly singular weak form integral equations for the displacement and traction on the boundary of the domain these integral equations are solved approximately using standard galerkin approximation in addition to the advantages that iga owned the proposed method exploits the common boundary representation of cad model and boundary element method various numerical examples of both simple and complex geometries are examined to validate the accuracy and efficiency of the proposed method through the numerical examples it is observed that the iga sgbem produces highly accurate results

isogeometric finite element approximation of minimal surfaces based on extended loop subdivision in this paper we investigate the formulation of isogeometric analysis for minimal surface models on planar bounded domains by extended loop surface subdivision approach the exactness of the physical domain of interest is fixed on the coarsest level of the triangular discretization with any topological structure which is thought of as the initial control mesh of loop subdivision by performing extended loop subdivision the control mesh can be repeatedly refined and the geometry is described as an infinite set of quartic box spline while maintaining its original exactness the limit function representation of extended loop subdivision forms our finite element space which possesses c1 smoothness and the flexibility of mesh topology we establish its inverse inequalities which resemble the ones of general finite element spaces we develop the approximation estimate with the aid of h1 convergence property of the corresponding linear models it enables us to overcome the difficulty of proving the boundedness of the gradient of finite element solutions appearing in the coefficient of minimal surface models numerical examples are given with the comparison to the classical linear finite element method which is consistent with our theoretical results

robust stability of time delay systems with an uncertain time delay constant frequency domain methods are described for testing the robust stability of a class of time delay systems with an uncertain time constant both parametric and non parametric uncertainties are considered our technique determines without a sweep of time delay the maximum time delay constant which preserves the robust stability

a constrained reproducing kernel particle formulation for shear deformable shell in cartesian coordinates the meshfree approximation functions for shell analysis to date are formulated using parametric coordinates and this parametric description of shell kinematics limits the applications only to shell structures with simple geometries on the other hand construction of moving least square or reproducing kernel rk approximation on shell surface using cartesian coordinates leads to a singular system when rk basis functions and shell surface function are linearly dependent in this study a constrained rk approximation formulated under cartesian coordinate for approximation of shell kinematics in arbitrary shell geometry is proposed two methods the dummy node approach and the pseudo inverse method are presented further stabilization of nodal integration for solving shear deformable shell is introduced the performance of present formulation is demonstrated in several benchmark problems copyright 2006 john wiley sons ltd

a hybrid variational collocation immersed method for fluid structure interaction using unstructured t splines summary we present a hybrid variational collocation immersed and fully implicit formulation for fluid structure interaction fsi using unstructured t splines in our immersed methodology we define an eulerian mesh on the whole computational domain and a lagrangian mesh on the solid domain which moves arbitrarily on top of the eulerian mesh mathematically the problem reduces to solving three equations namely the linear momentum balance mass conservation and a condition of kinematic compatibility between the lagrangian displacement and the eulerian velocity we use a weighted residual approach for the linear momentum and mass conservation equations but we discretize directly the strong form of the kinematic relation deriving a hybrid variational collocation method we use t splines for both the spatial discretization and the information transfer between the eulerian mesh and the lagrangian mesh t splines offer us two main advantages against non uniform rational b splines they can be locally refined and they are unstructured the generalized method is used for the time discretization we validate our formulation with a common fsi benchmark problem achieving excellent agreement with the theoretical solution an example involving a partially immersed solid is also solved the numerical examples show how the use of t junctions and extraordinary nodes results in an accurate efficient and flexible method copyright 2015 john wiley sons ltd

an isogeometric meshfree coupling approach for analysis of cracks summary this paper presents a new concurrent simulation approach to couple isogeometric analysis iga with the meshfree method for studying of crack problems in the present method the overall physical domain is divided into two sub domains which are formulated with the iga and meshfree method respectively in the meshfree sub domain the moving least squares mls shape function is adopted for the discretization of the area around crack tips and the iga sub domain is adopted in the remaining area meanwhile the interface region between the two sub domains is represented by coupled shape functions the resulting shape function which comprises both iga and meshfree shape functions satisfies the consistency condition thus ensuring convergence of the method moreover the meshfree shape functions augmented with the enriched basis functions to predict the singular stress fields near a crack tip are presented the proposed approach is also applied to simulate the crack propagation under a mixed mode condition several numerical examples are studied to demonstrate the utility and robustness of the proposed method this article is protected by copyright all rights reserved

rectified unstructured t splines with dynamic weighted refinement for improvement in geometric consistency and approximation convergence abstract t splines developed on unstructured meshes are called unstructured t splines which have the problem of geometric inconsistency and unfairness of mesh density evolution over regular or irregular elements during the refinement geometric inconsistency means that the geometry defined by an unstructured t spline keeps changing throughout the refinement the unfairness of mesh density evolution pertains to different scalings of regular and irregular elements during the refinement which drags down the convergence of the approximation result in isogeometric analysis this paper proposes rectified unstructured t splines to solve these two problems with the dynamic weighted refinement and rectified t spline basis functions owing to the dynamic weighted refinement the mesh size scaling tends to 1 2 fairly everywhere on unstructured meshes and geometric consistency is improved with the rectified t spline basis functions the approximation convergence is also greatly enhanced for isogeometric analysis from the original unstructured t splines which is quite meaningful for engineering simulations

approximation of cahn hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with c1 elements a variational formulation and c1 finite element scheme with adaptive mesh refinement and coarsening are developed for phase separation processes described by the cahn hilliard diffuse interface model of transport in a mixture or alloy the adaptive scheme is guided by a laplacian jump indicator based on the corresponding term arising from the weak formulation of the fourth order non linear problem and is implemented in a parallel solution framework it is then applied to resolve complex evolving interfacial solution behavior for 2d and 3d simulations of the classic spinodal decomposition problem from a random initial mixture and to other phase transformation applications of interest simulation results and adaptive performance are discussed the scheme permits efficient robust multiscale resolution and interface characterization copyright 2008 john wiley sons ltd

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

implicit dynamic analysis using an isogeometric reissner mindlin shell formulation summary in isogeometric analysis identical basis functions are used for geometrical representation and analysis in this work non uniform rational basis splines basis functions are applied in an isoparametric approach an isogeometric reissner mindlin shell formulation for implicit dynamic calculations using the galerkin method is presented a consistent as well as a lumped matrix formulation is implemented the suitability of the developed shell formulation for natural frequency analysis is demonstrated by a numerical example in a second set of examples transient problems of plane and curved geometries undergoing large deformations in combination with nonlinear material behavior are investigated via a zero thickness stress algorithm for arbitrary material models a j2 plasticity constitutive law is implemented in the numerical examples the effectiveness robustness and superior accuracy of a continuous interpolation method of the shell director vector is compared with experimental results and alternative numerical approaches copyright 2016 john wiley sons ltd

geometry independent field approximation cad analysis integration geometrical exactness and adaptivity in isogeometric analysis iga the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain this identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper 20 as a key advantage on the way to the integration of computer aided design cad and subsequent analysis in computer aided engineering cae 20 claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables without requiring the regeneration of the mesh at each change of the domain geometry yet in finite element versions of iga a parameterization of the interior of the domain must still be constructed since cad only provides information about the boundary the identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately in particular when the solution is not smooth we propose here a new paradigm called geometry independent field approximation gift where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight cad integration gift has the following features 1 it is possible to flexibly

dimensions of spline spaces over t meshes a t mesh is basically a rectangular grid that allows t junctions in this paper we propose a method based on bezier nets to calculate the dimension of a spline function space over a t mesh when the order of the smoothness is less than half of the degree of the spline functions a dimension formula is derived which involves only the topological quantities of the t mesh the construction of basis functions is briefly discussed furthermore the dimension formulae for t meshes after mesh operations such as edge insertion and mesh merging are also obtained

an alternative alpha finite element method aαfem for free and forced structural vibration using triangular meshes an alternative alpha finite element method email protected using triangular elements is proposed that significantly improves the accuracy of the standard triangular finite elements and provides a superconvergent solution in the energy norm for the static analysis of two dimensional solid mechanics problems in the email protected the piecewise constant strain field of linear triangular fem models is enhanced by additional strain terms with an adjustable parameter a which results in an effectively softer stiffness formulation compared to a linear triangular element the element is further extended to the free and forced vibration analyses of solids several numerical examples show that the email protected achieves high reliability compared to other existing elements in the literature

smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points geometric design and isogeometric analysis considerations abstract we present a framework for geometric design and isogeometric analysis on unstructured quadrilateral meshes acknowledging the differing requirements posed by design e g the convenience of an intuitive control net and analysis e g good approximation behavior we propose the construction of a separate smooth spline space for each while ensuring isogeometric compatibility requiring the geometric models to be members of the analysis suitable spaces the methodology is simple and is presented for bi cubic splines extensions to higher degrees are possible and are briefly discussed the presentation has been structured to show compatibility with t splines a state of the art cad technology but the approach should extend to other locally refinable spline technologies based on local tensor product structures an instantiation of the framework is presented and several numerical tests focused on geometric design and isogeometric analysis demonstrate the versatility of the developed framework and show significantly higher convergence rates than attained previously in the considered setting

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

goal adaptive isogeometric analysis with hierarchical splines abstract in this work a method of goal adaptive isogeometric analysis is proposed we combine goal oriented error estimation and adaptivity with hierarchical b splines for local h refinement the goal oriented error estimator is computed with a p refined discrete dual space which is adaptively refined alongside the primal space this discrete dual space is proven to be a strict superset of the primal space hierarchical refinements are introduced in marked regions that are formed as the union of chosen coarse level spline supports from the primal basis we present two ways of extracting localized refinement indicators suitable for the hierarchical refinement procedure one based on a partitioning of the dual weighted residual into contributions of basis function supports and one based on the combination of element indicators within a basis function support the proposed goal oriented adaptive strategy is exemplified for the poisson problem and a free surface flow problem numerical experiments on these problems show convergence of the adaptive method with optimal rates furthermore the corresponding goal oriented error estimators are shown to be accurate with effectivity indices in the range of 0 7 1 1

reproducing kernel triangular b spline based fem for solving pdes abstract we propose a reproducing kernel triangular b spline based finite element method fem as an improvement to the conventional triangular b spline element for solving partial differential equations pdes in the latter unexpected errors can occur throughout the analysis domain mainly due to the excessive flexibilities in defining the b spline the performance therefore becomes unstable and cannot be controlled in a desirable way to address this issue the proposed improvement adopts the reproducing kernel approximation in the calculation of b spline kernel function three types of pde problems are tested to validate the present element and compare against the conventional triangular b spline it has been shown that the improved triangular b spline satisfies the partition of unity condition even for extreme conditions including corners and holes

stabilization of vibration systems via delayed state difference feedback this paper presents a study of the stabilization problem via delayed state feedback of pyragas type for unstable vibration systems that have even number of characteristic roots with positive real parts on the basis of stability switches with respect to the time delay a new stabilization criterion is established and an effective procedure for determining the admissible values of the feedback gains and the delay is given two examples are given in detail to demonstrate the efficiency of the theory

bifurcations of a generalized van der pol oscillator with strong nonlinearity a generalized van der pol oscillator with parametric excitation is studied for its bifurcation on the basis of the mlp method we enable a strongly nonlinear system to be transformed into a small parameter system the bifurcation response equation of a 1 2 subharmonic resonance system is determined by the multiple scales method according to the singularity theory the bifurcation of equilibrium points is analyzed the stability of the zero solution is researched by the eigenvalues of the variational matrix and the bifurcation sets are constructed in various regions of the parameter plane

thin shell analysis from scattered points with maximum entropy approximants this is the accepted version of the following article millan d rosolen a and arroyo m 2011 thin shell analysis from scattered points with maximum entropy approximants int j numer meth engng 85 723 751 doi 10 1002 nme 2992 which has been published in final form at http onlinelibrary wiley com doi 10 1002 nme 2992 abstract

weak coupling for isogeometric analysis of non matching and trimmed multi patch geometries nitsche s method can be used as a coupling tool for non matching discretizations by weakly enforcing interface constraints we explore the use of weak coupling based on nitsche s method in the context of higher order and higher continuity b splines and nurbs we demonstrate that weakly coupled spline discretizations do not compromise the accuracy of isogeometric analysis we show that the combination of weak coupling with the finite cell method opens the door for a truly isogeometric treatment of trimmed b spline and nurbs geometries that eliminates the need for costly reparameterization procedures we test our methodology for several relevant technical problems in two and three dimensions such as gluing together trimmed multi patches and connecting non matching meshes that contain b spline basis functions and standard triangular finite elements the results demonstrate that the concept of nitsche based weak coupling in conjunction with the finite cell method has the potential to considerably increase the flexibility of the design through analysis process in isogeometric analysis

a finite element scheme with the aid of a new carving technique combined with smoothed integration abstract an efficient scheme is proposed that can generate appropriate meshes for three dimensional complex domains leading to accurate solutions in finite element analysis after preparing a structured mesh with hexahedral elements the surface information of an arbitrary domain is soaked into the mesh the elements around the surface are trimmed according to the surface information and then they are replaced by polyhedral elements while the interior of the domain remains occupied by the original hexahedral elements the scheme is further extended to manage complex domains with discontinuities in geometry and material properties such as a polycrystalline structure comprised of multiple materials or grains as well as highly curved domains with a single material subsequently the generated mesh composed of the polyhedral elements on the surface and the hexahedral elements in the interior is directly applied for finite element analysis in conjunction with smoothed integration in the strain smoothing technique because the smoothed integration does not require the shape function derivatives the efficient analysis can be conducted without explicitly defined shape functions of the polyhedral elements the smoothed integration can improve the accuracy of the numerical solutions as well the present study focuses on reporting a new idea on a finite element scheme using the polyhedral elements with the smoothed integration rather than providing a general and systematic approach however it has a great potential to deal with general and practical problems through numerical examples it is shown that the proposed scheme provides accurate solutions in a simple and efficient manner

mathematical analysis and numerical study to free vibrations of annular plates using biem and bem in this paper the spurious eigenequations for annular plate eigenproblems by using biem and bem are studied in the continuous and discrete systems since any two boundary integral equations in the plate formulation 4 equations can be chosen 6 c options can be considered instead of only two approaches single layer and double layer methods or singular and hypersingular equations which are adopted for the eigenproblems of the membrane and acoustic problems the occurring mechanism of the spurious eigenequation for annular plates in the complex valued formulations is studied analytically for the continuous system degenerate kernels for the fundamental solution and the fourier series expansion for the circular boundary density are employed to derive the true and spurious eigenequations analytically for the discrete system the degenerate kernels for the fundamental solution and circulants resulting from the circular boundary are employed to determine the true and spurious eigenequations true eigenequation depends on the specified boundary condition while spurious eigenequation is embedded in each formulation it is found that the spurious eigenvalue for the annular plate is the true eigenvalue of the associated interior problem with an inner radius of the annular domain also we provide three methods svd updating technique burton and miller method and chief method to suppress the occurrence of the spurious eigenvalues several examples were demonstrated to check the validity of the formulations copyright 2005 john wiley sons ltd

multi patch nonsingular isogeometric boundary element analysis in 3d abstract a multi patch nonsingular isogeometric boundary element method igabem for 3d problems is presented that provides accurate solutions for multi patch igabem in order to conveniently implement this method based on the greville abscissae a new collocation method moves the first and the last collocation points of each parametric direction inside of their patches and a simple method for merging equations handles the extra equations the numerical results verify the accuracy and efficiency of the present method by comparing it to the conventional igabem

isogeometric collocation for large deformation elasticity and frictional contact problems abstract isogeometric collocation methods have been recently proposed as an alternative to standard galerkin approaches as they provide a significant reduction in computational cost for higher order discretizations in this work we explore the application of isogeometric collocation to large deformation elasticity and frictional contact problems we first derive the non linear governing equations for the elasticity problem with finite deformation kinematics and provide details on their consistent linearization some numerical examples demonstrate the performance of collocation in its basic and enhanced versions differing by the enforcement of neumann boundary conditions for problems with strong singularities enhanced collocation is shown to outperform basic collocation and to lead to a spatial convergence behavior very similar to galerkin whereas for weaker or no singularities enhanced and basic collocation may give very similar results a large deformation contact formulation is subsequently developed and tested in the frictional setting where collocation confirms the excellent performance already obtained for the frictionless case finally it is shown that the contact formulation in the collocation framework passes the contact patch test to machine precision in a three dimensional setting with arbitrarily inclined non matching discretizations thus outperforming most of the available contact formulations and all those with pointwise enforcement of the contact constraints

robust stability for time delay systems the edge theorem and graphical tests the robust stability problem is discussed for a class of uncertain delay systems where the characteristic equations involve a polytope p of quasi polynomials i e polynomials in one complex variable and exponential powers of the variable given a set d in the complex plane the goal is to find a constructive technique to verify whether all roots of every quasi polynomial in p belong to d that is to verify the d stability of p first it is demonstrated by counterexample that kharitonov s theorem does not hold for general delay systems next it is shown that under a mild assumption on the set d a polytope of quasi polynomials is d stable if and only if the edges of the polytope are d stable this extends the edge theorem for the d stability of a polytope of polynomials the third result gives a constructive graphical test for checking the d stability of a polytope of quasi polynomials which is especially simple when the set d is the open left half plane an application is given to demonstrate the power of the results

embedded structural entities in nurbs based isogeometric analysis the core idea of this article is nested parametrization in the context of isogeometric analysis the method has been inspired by trimming procedures and can be applied to different applications like local modifications and enhancements of thin walled structures or coupling of two overlying elements by embedding one in the other a remodeling for an explicit representation of the boundaries is avoided which would be contradictory to the aim of isogeometric analysis of using the original cad model the nested entity is directly linked to the super element however its element formulation is independent of the super element formulation within this article the derivation implementation and application is shown in particular for one dimensional entities embedded into 2d domains consequently the definition of an embedded curve in the surface is required and realized by using nurbs curves in the parameter space of the corresponding surface this curve with its respective predefined base vectors serves as the basis for new element formulations or adaptation of already developed element formulations which are based on the geometric description of a curve in detail an adapted formulation of the recently developed nonlinear isogeometric spatial bernoulli beam by the authors is presented in this paper furthermore those embedded curves are used for line supports and loads as well as a mass manipulation the accuracy of the proposed element formulation is verified by several benchmark examples and the potential for future applications is briefly revealed

h and p adaptivity driven by recovery and residual based error estimators for pht splines applied to time harmonic acoustics abstract in this work we demonstrate the application of pht splines for time harmonic acoustic problems modeled by the helmholtz equation solutions of the helmholtz equation have two features global oscillations associated with the wave number and local gradients caused by geometrical irregularities we show that after a sufficient number of degrees of freedom is used to approximate global oscillations adaptive refinement can capture local features of the solution we compare residual based and recovery based error estimators and investigate the performance of p refinement the simulations are done in the context of recently introduced geometry independent field approximation gift where pht splines are only used to approximate the solution while the computational domain is parameterized with nurbs this approach builds on the natural adaptation ability of pht splines and avoids the re parameterization of the nurbs geometry during the solution refinement process

a smoothed finite element method for plate analysis a quadrilateral element with smoothed curvatures for mindlin reissner plates is proposed the curvature at each point is obtained by a non local approximation via a smoothing function the bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements smoothing cells numerical results show that the proposed element is robust computational inexpensive and simultaneously very accurate and free of locking even for very thin plates the most promising feature of our elements is their insensitivity to mesh distortion

a new discontinuous galerkin method for kirchhoff love shells abstract discontinuous galerkin methods dg have particular appeal in problems involving high order derivatives since they provide a means of weakly enforcing the continuity of the unknown field derivatives this paper proposes a new discontinuous galerkin method for kirchhoff love shells considering only the membrane and bending response the proposed one field method utilizes the weak enforcement in such a way that the displacements are the only unknowns while the rotation continuity is weakly enforced this work presents the formulation of the new discontinuous galerkin method for linear elastic shells demonstrates the consistency and stability of the proposed framework and establishes the method s convergence rate after a description of the formulation implementation into a finite element code these properties are demonstrated on numerical applications

isogeometric analysis for surface pdes with extended loop subdivision abstract we investigate the isogeometric analysis for surface pdes based on the extended loop subdivision approach the basis functions consisting of quartic box splines corresponding to each subdivided control mesh are utilized to represent the geometry exactly and construct the solution space for dependent variables as well which is consistent with the concept of isogeometric analysis the subdivision process is equivalent to the h refinement of nurbs based isogeometric analysis the performance of the proposed method is evaluated by solving various surface pdes such as surface laplace beltrami harmonic biharmonic triharmonic equations which are defined on the limit surfaces of extended loop subdivision for different initial control meshes numerical experiments show that the proposed method has desirable performance in terms of the accuracy convergence and computational cost for solving the above surface pdes defined on both open and closed surfaces the proposed approach is proved to be second order accuracy in the sense of l 2 norm with theoretical and or numerical results which is also outperformed over the standard linear finite element by several numerical comparisons

a natural framework for isogeometric fluid structure interaction based on bem shell coupling abstract the interaction between thin structures and incompressible newtonian fluids is ubiquitous both in nature and in industrial applications in this paper we present an isogeometric formulation of such problems which exploits a boundary integral formulation of stokes equations to model the surrounding flow and a non linear kirchhoff love shell theory to model the elastic behavior of the structure we propose three different coupling strategies a monolithic fully implicit coupling a staggered elasticity driven coupling and a novel semi implicit coupling where the effect of the surrounding flow is incorporated in the non linear terms of the solid solver through its damping characteristics the novel semi implicit approach is then used to demonstrate the power and robustness of our method which fits ideally in the isogeometric paradigm by exploiting only the boundary representation b rep of the thin structure middle surface

isogeometric analysis based on extended catmull clark subdivision in this paper we propose a subdivision based finite element method as an integration of the isogeometric analysis iga framework which adopts the uniform representation for geometric modeling and finite element simulation the finite element function space is induced from the limit form of catmull clark surface subdivision containing boundary subdivision schemes which has c 1 continuity everywhere it is capable of exactly representing complex geometries with any shaped boundaries which are represented as piecewise cubic b spline curves it is compatible with modern computer aided design cad software systems the advantage of this strategy admits quadrilateral meshes of arbitrary topology in this work the computational domains with planar geometries are considered we establish the approximation properties of catmull clark surface subdivision function based on the bramble hilbert lemma numerical tests are performed through three poisson s equations with the dirichlet boundary condition to corroborate the theoretical proof

spline spaces with mixed orders of continuity over t meshes in this paper we introduce the concept of spline spaces with mixed orders of continuity over t meshes then the dimensions of the cubic spline spaces with continuity of order one and locally discontinuous over hierarchical t meshes are presented by the b net method from the viewpoint of processing geometry data a non negative basis set with local support and partition of unity is constructed finally the behavior of this type of spline is analyzed with the help of examples in image processing and finite element analysis

form finding with dynamic relaxation and isogeometric membrane elements a method for form finding with dynamic relaxation and non uniform rational b splines nurbs based isogeometric membrane elements has been implemented and studied regarding the influence of the discretization and element shape on the form finding the procedure allows for rapid form finding since nurbs describe the curved geometry well and it is shown that the form finding can be performed using a coarse mesh however to minimize the bending strain energy a fine mesh is needed using smaller elements is more advantageous than increasing the degree of the basis functions keeping the number of integration points few and converging at a lesser number of iterations using isogeometric analysis iga simplifies further studies since the form found shape can be exactly represented with a shell element formulation the method is suitable to be used in computer aided design environments such as rhinoceros 3d during design stages where the form finding can be evaluated together with other studies in a design context

delay independent stability of retarded dynamic systems of multiple degrees of freedom on the basis of generalized sturm theory this paper presents a simple but systematic approach to the delay independent stability analysis of the linear dynamic systems involving multiple degrees of freedom and possibly two time delays the approach enables one to complete the stability analysis in a much simpler way than before through the use of a maple routine given in the paper to demonstrate the approach the paper gives a detailed analysis the corresponding sufficient and necessary conditions as well as stable regions in parameter space of concern for the delay independent stability of a vibrating system with time delays in state feedback an active tendon for a tall structure and an active suspension of a quarter car model

robust stability of time delay systems there are two fundamental results available when we study stability of a polynomial family that is described by convex polytope in the coefficient space the edge theorem and the theory based on the concept of convex directions many known results can be explained with these two results this paper deals with a generalization of this line of research to the case of quasipolynomials that are entire functions which include both degree of the independent variable and exponential functions the main objects of the paper are the developing of the concept of convex directions for quasipolynomials and exploiting this concept for construction of testing sets for quasipolynomial families one of the primary sources of motivation for the class of problems considered in this paper is derived from process control a typical problem formulation almost always includes a delay element in each subsystem process block when we interconnect a number of such blocks in a feedback system the study of robust stability involves quasipolynomials of the sort considered in this paper

t spline finite element method for the analysis of shell structures a t spline surface is a nonuniform rational b spline nurbs surface with t junctions and is defined by a control grid called t mesh the t mesh is similar to a nurbs control mesh except that in a t mesh a row or column of control points is allowed to terminate in the inner parametric space this property of t splines makes local refinement possible in the present study shell formulation based on the t spline finite element method fem is presented shell formulation based on nurbs or t splines has fundamental limitations because rotational dofs which are necessary in the shell formulation cannot be defined on control points in this study the simple mapping scheme in which every control point is mapped into one geometric point on the surface is employed to eliminate the limitations using this mapping scheme t spline fem can be easily extended to the analysis of shells the proposed shell formulation is verified through various benchmarking problems this study is a part of the efforts by the authors for the integration of cad cae processes

variationally consistent domain integration for isogeometric analysis abstract spline type approximations for solving partial differential equations are the basis of isogeometric analysis while the common approach of using integration cells defined by single knot spans using standard e g gaussian quadrature rules is sufficient for accuracy more efficient domain integration is still in high demand the recently introduced concept of variational consistency provides a guideline for constructing accurate and convergent methods requiring fewer quadrature points than standard integration techniques in this work variationally consistent domain integration is proposed for isogeometric analysis test function gradients are constructed to meet the consistency conditions which only requires solving small linear systems of equations the proposed approach allows for significant reduction in the number of quadrature points employed while maintaining the stability accuracy and optimal convergence properties of higher order quadrature rules several numerical examples are provided to illustrate the performance of the proposed domain integration technique

stability criteria for linear time invariant systems with point delays based on one dimensional routh hurwitz tests this brief deals with the asymptotic stability of a class of linear time invariant systems subject to point constant uncommensurate delays results are obtained dependent on and independent of the delays which may be tested be performing a finite set of 1 d routh hurwitz tests on a corresponding set of auxiliary delay free linear time invariant systems plus some supplementary conditions related to either commutation pairwise of the associate dynamics matrices or their norm closeness or some simple testable conditions if the matrices have particular forms and there is only one single delay the obtained results are applicable to the case when a finite set of matrices describing the dynamics of a set of delay free auxiliary dynamical systems are hurwitz and either commute pair wise or their norms are sufficiently close to each other some extensions are given to robust stability of point time delay time invariant systems with commensurate delays parametrized by an uncertain parameter vector whose components are in real intervals of known limits

initial solution estimation for one step inverse isogeometric analysis in sheet metal stamping abstract recently isogeometric analysis iga based on incremental methods for simulating the stamping process has been researched to the best of our knowledge however few studies have combined iga and one step inverse approach which is based on total deformation theory of plasticity a key step for one step inverse iga is to estimate a good initial solution traditional mesh based initial solution algorithms for one step inverse approach are not suitable for one step inverse nurbs based iga in this paper we presented a method which can rapidly unfold the undevelopable nurbs surface onto a planar domain and obtain a good initial solution estimation for one step inverse iga the key idea of the presented method is unfolding the control net of a nurbs surface for isogeometric analysis by energy based initial solution estimation algorithm in addition we developed a cutting stitching algorithm which can separate a complex control net into several parts with simple shapes numerical examples illustrate the initial solutions using the presented method are approaching the final results by one step inverse finite element method this implies that the iterative steps and computational time of one step inverse iga will be reduced significantly compared with that of one step inverse finite element method

counting roots of the characteristic equation for linear delay differential systems abstract a formula is given that counts the number of roots in the positive half plane of the characteristic equation for general real constant coefficient linear delay differential systems the formula is used to establish necessary and sufficient conditions for asymptotic stability of the zero solution of linear delay differential systems the formula is potentially useful in verifying stability hypotheses that arise in bifurcation analysis of autonomous delay differential systems application of the formula to hopf bifurcation theory for delay differential systems is discussed and an example application to an equation with two delays is given

robust stabilization of a class of polytopic linear time varying continuous systems under point delays and saturating controls abstract this paper investigates the stabilization dependent on the delays of in general time varying linear systems with multiple constant point time delays under saturating state feedback controls the matrices describing the state space dynamics and control belong to polytopes also the controller gain matrix is characterized as belonging to another polytope whose vertices are computed from the knowledge of a closed bounded ball containing a set of values of the state norm and also the component wise saturating gains and saturation parameterizations this knowledge defines the polytope vertices through scaling diagonal matrices being associated with the various operation modes in the linear and saturated zones of each input component in these conditions the resulting closed loop system is of polytopic nature whose whole number of vertices is at most equal to the product of both numbers of vertices of the above two polytopes characterizing the plant parameterization and the saturation the closed loop sufficiency type stability conditions are obtained from lyapunov s stability theory by constructing candidates for each vertex of the polytopic closed loop system each satisfying in the most general case a riccati matrix differential inequality some conditions guaranteeing the stability conditions are obtained from a general kalman yakubovitch popov kyp lemma and some weaker stability conditions are also obtained for the time invariant case from a set of linear matrix inequalities associated with the set of vertices