a fully locking free isogeometric approach for plane linear elasticity problems a stream function formulation in this paper we study plane incompressible elastic problems by means of a stream function formulation such that a divergence free displacement field can be computed from a scalar potential the numerical scheme is constructed within the framework of nurbs based isogeometric analysis and we take advantage of the high continuity guaranteed by nurbs basis functions in order to obtain the displacement field from the potential differentiation as a consequence the obtained numerical scheme is automatically locking free in the presence of the incompressibility constraint a discontinuous galerkin approach is proposed to deal with multiple mapped possibly multiply connected domains extensive numerical results are provided to show the method capabilities 2007 elsevier b v all rights reserved

automated fuzzy and probabilistic inference abstract this paper illustrates the use of fril in the solution of inference problems under uncertainty and certain recursive functional equations various aspects of fril discussed include depth and breadth strategies backtracking mechanism and relational algebraic operation examples of the application of the theory to expert systems and decision support systems are provided

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

the post processing approach in the finite element method part 1 calculation of displacements stresses and other higher derivatives of the displacements this is the first in a series of three papers in which we discuss a method for post processing a finite element solution to obtain high accuracy approximations for displacements stresses stress intensity factors etc rather than take the values of these quantities directly from the finite element solution we evaluate certain weighted averages of the solution over the entire region these yield approximations are of the same order of accuracy as the strain energy we obtain error estimates and also present some numerical examples to illustrate the practical effectiveness of the technique in the third paper of this series we address the matters of adaptive mesh selection and a posteriori error estimation

the finite cell method for three dimensional problems of solid mechanics this article presents a generalization of the recently proposed finite cell method to three dimensional problems of linear elasticity the finite cell method combines ideas from embedding or fictitious domain methods with the p version of the finite element method besides supporting a fast simple generation of meshes it also provides high convergence rates mesh generation for a boundary representation of solids and for voxel based data obtained from ct scans is addressed in detail in addition the implementation of non homogeneous neumann boundary conditions and the computation of cell matrices based on a composed integration is presented the performance of the proposed method is demonstrated by three numerical examples including the elastostatic computation of a human bone biopsy

l and l 2 semi global stabilisation of continuous time periodic linear systems with bounded controls this article is concerned with l and l 2 semi global stabilisation of continuous time periodic linear systems with bounded controls two problems namely l semi global stabilisation with controls having bounded magnitude and l 2 semi global stabilisation with controls having bounded energy are solved based on solutions to a class of periodic lyapunov differential equations pldes resulting from the problem of minimal energy control with guaranteed convergence rate under the assumption that the open loop system is asymptotically null controllable with constrained controls periodic feedback are established to solve the concerned problems the proposed plde based approaches possess the advantage that the resulting controllers are easy to implement since the designers need only to solve a linear differential equation a numerical example is worked out to illustrate the effectiveness of the proposed approach

a generalised pid type control scheme with simple tuning for the global regulation of robot manipulators with constrained inputs in this paper a globally stabilising pid type control scheme with a generalised saturating structure for robot manipulators under input constraints is proposed it gives rise to various families of bounded pid type controllers whose implementation is released from the exact knowledge of the system parameters and model structure compared to previous approaches of the kind the proposed scheme is not only characterised by its generalised structure but also by its very simple tuning criterion the simplest hitherto obtained in the considered analytical framework experimental results on a 3 degree of freedom direct drive manipulator corroborate the efficiency of the proposed approach

a new face oriented stabilized xfem approach for 2d and 3d incompressible navier stokes equations abstract we develop a new stabilized xfem based fixed grid approach for the transient incompressible navier stokes equations using cut elements our framework is based on a new flexible strategy to handle several degrees of freedom dofs at nodes required for complex shaped embedded meshes as they occur for fixed grid fluid structure interaction problems boundary conditions on embedded boundaries are imposed weakly using a nitsche type approach ghost penalty terms for velocity and pressure are added for stability reasons and to improve the conditioning of the system matrix the idea of ghost penalties previously developed for stokes problems is extended to the incompressible navier stokes equations by using face oriented fluid stabilizations for both viscous and convective dominated flows furthermore the need for additional terms to enforce boundary conditions for non viscous flows is addressed a detailed numerical study of our stabilized fluid formulation including studies of nitsche s parameter and the ghost penalty parameter shows optimal error convergence and a good system conditioning in the viscous and the convective dominated cases compared to other fixed grid fluid formulations our method is much more accurate and less sensitive to the location of the interface regarding the accuracy and the sensitivity with respect to the interface position a clear improvement could be observed for the viscous and pressure fluxes as well as for the imposition of the boundary condition results of a transient two dimensional high reynolds number flow over a cylinder and the flow over a thick plate in 3d confirm the applicability of the proposed method

skeleton stabilized immersogeometric analysis for incompressible viscous flow problems a skeleton stabilized immersogeometric analysis technique is proposed for incompressible viscous flow problems with moderate reynolds numbers the proposed formulation fits within the framework of the finite cell method where essential boundary conditions are imposed weakly using a nitsche type method the key idea of the proposed formulation is to stabilize the jumps of high order derivatives of variables over the skeleton of the background mesh the formulation allows the use of identical finite dimensional spaces for the approximation of the pressure and velocity fields in immersed domains the stability issues observed for inf sup stable discretizations of immersed incompressible flow problems are avoided with this formulation for b spline basis functions of degree formula presented with highest regularity only the derivative of order formula presented has to be controlled which requires specification of only a single stabilization parameter for the pressure field the stokes and navier stokes equations are studied numerically in two and three dimensions using various immersed test cases oscillation free solutions and high order optimal convergence rates can be obtained the formulation is shown to be stable even in limit cases where almost every elements of the physical domain is cut and hence it does not require the existence of interior cells in terms of the sparsity pattern the algebraic system has a considerably smaller stencil than counterpart approaches based on lagrange basis functions this important property makes the proposed skeleton stabilized technique computationally practical to demonstrate the stability and robustness of the method we perform a simulation of fluid flow through a porous medium of which the geometry is directly extracted from 3d formula presented scan data

an unfitted hp adaptive finite element method based on hierarchical b splines for interface problems of complex geometry generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries the paper at hand introduces a b spline finite element method which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement which adds several levels of local basis functions in the close vicinity of interfaces but unfitted to their exact location so that a simple regular grid of knot span elements can be maintained numerical experiments show that an hp refinement strategy which simultaneously increases the polynomial degree of the b spline basis and the levels of refinement around interfaces achieves exponential rates of convergence despite the presence of discontinuities it is also demonstrated that the hierarchical b spline fem can be used to transfer the recently introduced finite cell concept to geometrically nonlinear problems its computational performance imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one two and three dimensions and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite

subdivision stabilised immersed b spline finite elements for moving boundary flows an immersed finite element method is presented to compute flows with complex moving boundaries on a fixed cartesian grid the viscous incompressible fluid flow equations are discretized with b spline basis functions the two scale relation for b splines is used to implement an elegant and efficient technique to satisfy the lbb condition on non grid aligned fluid domains and at moving boundaries the boundary conditions are enforced with a consistent penalty method as originally proposed by nitsche in addition a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut cells the versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations

skeleton stabilized isogeometric analysis high regularity interior penalty methods for incompressible viscous flow problems abstract a skeleton stabilized isogeometric analysis siga technique is proposed for incompressible viscous flow problems with moderate reynolds number the proposed method allows utilizing identical finite dimensional spaces with arbitrary b splines nurbs order and regularity for the approximation of the pressure and velocity components the key idea is to stabilize the jumps of high order derivatives of variables over the skeleton of the mesh for b splines nurbs basis functions of degree k with c regularity 0 k only the derivative of order 1 has to be controlled this stabilization technique thus can be viewed as a high regularity generalization of the continuous interior penalty finite element method numerical experiments are performed for the stokes and navier stokes equations in two and three dimensions oscillation free solutions and optimal convergence rates are obtained in terms of the sparsity pattern of the algebraic system we demonstrate that the block matrix associated with the stabilization term has a considerably smaller bandwidth when using b splines than when using lagrange basis functions even in the case of c 0 continuity this important property makes the proposed isogeometric framework practical from a computational effort point of view

mixed isogeometric finite cell methods for the stokes problem we study the application of the isogeometric finite cell method iga fcm to mixed formulations in the context of the stokes problem we investigate the performance of the iga fcm when utilizing some isogeometric mixed finite elements namely taylor hood sub grid raviart thomas and nedelec elements these element families have been demonstrated to perform well in the case of conforming meshes but their applicability in the cut cell context is still unclear dirichlet boundary conditions are imposed by nitsche s method numerical test problems are performed with a detailed study of the discrete inf sup stability constants and of the convergence behavior under uniform mesh refinement

a stabilized nitsche cut finite element method for the oseen problem abstract we provide the numerical analysis for a nitsche based cut finite element formulation for the oseen problem which has been originally presented for the incompressible navier stokes equations by schott and wall 2014 and allows the boundary of the domain to cut through the elements of an easy to generate background mesh the formulation is based on the continuous interior penalty cip method of burman et al 2006 which penalizes jumps of velocity and pressure gradients over inter element faces to counteract instabilities arising for high local reynolds numbers and the use of equal order interpolation spaces for the velocity and pressure since the mesh does not fit the boundary dirichlet boundary conditions are imposed weakly by a stabilized nitsche type approach the addition of cip like ghost penalties in the boundary zone allows to prove that our method is inf supstable and to derive optimal order a priori error estimates in an energy type norm irrespective of how the boundary cuts the underlying mesh all applied stabilization techniques are developed with particular emphasis on low and high reynolds numbers two and three dimensional numerical examples corroborate the theoretical findings finally the proposed method is applied to solve the transient incompressible navier stokes equations on a complex geometry

edge stabilization for the generalized stokes problem a continuous interior penalty method in this note we introduce and analyze a stabilized finite element method for the generalized stokes equation stability is obtained by adding a least squares penalization of the gradient jumps acro

a note on the stability parameter in nitsche s method for unfitted boundary value problems abstract nitsche s method is a popular approach to implement dirichlet type boundary conditions in situations where a strong imposition is either inconvenient or simply not feasible the method is widely applied in the context of unfitted finite element methods of the classical symmetric nitsche s method it is well known that the stabilization parameter in the method has to be chosen sufficiently large to obtain unique solvability of discrete systems in this short note we discuss an often used strategy to set the stabilization parameter and describe a possible problem that can arise from this we show that in specific situations error bounds can deteriorate and give examples of computations where nitsche s method yields large and even diverging discretization errors

a stabilised immersed boundary method on hierarchical b spline grids abstract in this work an immersed boundary finite element method is proposed which is based on a hierarchically refined cartesian b spline grid and employs the non symmetric and penalty free version of nitsche s method to enforce the boundary conditions the strategy allows for h and p refinement and employs a so called ghost penalty term to stabilise the cut cells an effective procedure based on hierarchical subdivision and sub cell merging which avoids excessive numbers of quadrature points is used for the integration of the cut cells a basic laplace problem is used to demonstrate the effectiveness of the cut cell stabilisation and of the penalty free nitsche method as well as their impact on accuracy the methodology is also applied to the incompressible navier stokes equations where the supg pspg stabilisation is employed simulations of the lid driven cavity flow and the flow around a cylinder at low reynolds number show the good performance of the methodology excessive ill conditioning of the system matrix is robustly avoided without jeopardising the accuracy at the immersed boundaries or in the field

geometric modeling isogeometric analysis and the finite cell method the advent of isogeometric analysis iga using the same basis functions for design and analysis constitutes a milestone in the unification of geometric modeling and numerical simulation however an important class of geometric models based on the csg constructive solid geometry concept such as trimmed nurbs surfaces do not fully support the isogeometric paradigm since basis functions do not explicitly represent the boundary the finite cell method fcm is a high order fictitious domain method which offers simple meshing of potentially complex domains into a structured grid of cuboid cells while still achieving exponential rates of convergence for smooth problems in the present paper we first discuss the possibility to directly couple the finite cell method to csg without any necessity for meshing the three dimensional domain and then explore a combination of the best of the two approaches iga and fcm closely following ideas of the recently introduced shell fcm the resulting finite cell extension to isogeometric analysis achieves a truly straightforward transfer of a trimmed nurbs surface into an analysis suitable nurbs basis while benefiting from the favorable properties of the high order and high continuity basis functions accuracy and efficiency of the new approach are demonstrated by a numerical benchmark and its versatility is outlined by the analysis of different trimmed design variants of a brake disk

on global output feedback regulation of euler lagrange systems with bounded inputs we identify a class of euler lagrange systems with bounded inputs that can be globally asymptotically stabilized via dynamic output feedback in particular we prove that if the system is fully actuated and the forces due to the potential field can be dominated by the constrained control signals then global output feedback regulation is still possible incorporating some suitable saturation functions in the controller

drag computation for incompressible flows with a nitsche s type stabilization method abstract we study the drag error for the navier stokes equations approximated by conforming low order finite elements the numerical scheme uses a supg stabilization and a new nitche s type stabilization on the whole boundary we introduce a definition of the discrete drag which contains additional terms resulting from the discrete formulat we prove o h 2 convergence for the drag error and illustrate the theoretical results by numerical tests the extension to other finite element methods is also discussed

image based goal oriented adaptive isogeometric analysis with application to the micro mechanical modeling of trabecular bone abstract isogeometric analysis iga of geometrically complex three dimensional objects is possible when used in combination with the finite cell method fcm in this contribution we propose a computational methodology to automatically analyze the effective elastic properties of scan based volumetric objects of arbitrary geometric and topological complexity the first step is the reconstruction of a smooth geometry from scan based voxel data using a b spline level set function the second step is a goal oriented adaptive isogeometric linear elastic analysis elements are selected for refinement using dual weighted residual shape function indicators and hierarchical splines are employed to construct locally refined spline spaces the proposed methodology is studied in detail for various numerical test cases including the computation of the effective young s modulus of a trabecular bone micro structure reproduced from ct scan data

brief semiglobal stability of saturated linear pid control for robot manipulators this paper addresses the position regulation problem of robot manipulators under control input constraints it is proven that the robot system under a saturated linear pid control is semiglobally asymptotically stable if the torque bounds are larger than gravitational torques and if the proportional gain is large enough and the integral gain is small enough the stability analysis makes use of singular perturbation tools and the results are illustrated via numerical simulations

error estimate based adaptive integration for immersed isogeometric analysis abstract the finite cell method fcm together with isogeometric analysis iga has been applied successfully in various problems in solid mechanics in image based analysis fluid structure interaction and in many other applications a challenging aspect of the isogeometric finite cell method is the integration of cut cells in particular in three dimensional simulations the computational effort associated with integration can be the critical component of a simulation a myriad of integration strategies has been proposed over the past years to ameliorate the difficulties associated with integration but a general optimal integration framework that suits a broad class of engineering problems is not yet available in this contribution we provide a thorough investigation of the accuracy and computational effort of the octree integration scheme we quantify the contribution of the integration error using the theoretical basis provided by strang s first lemma based on this study we propose an error estimate based adaptive integration procedure for immersed isogeometric analysis additionally we present a detailed numerical investigation of the proposed optimal integration algorithm and its application to immersed isogeometric analysis using two and three dimensional linear elasticity problems

isogeometric divergence conforming b splines for the unsteady navier stokes equations divergence conforming b splines are developed for application to the incompressible navier stokes equations on geometrically mapped domains these enable smooth pointwise divergence free solutions and thus satisfy mass conservation in the strongest possible sense semi discrete methods based on divergence conforming b splines are shown to conserve linear and angular momentum and satisfy balance laws for energy vorticity enstrophy and helicity these are geometric structure preserving quantities and numerical simulations that are sensitive to them are shown to be qualitatively correct and quantitatively accurate the methods developed are anticipated to open new doors to the practical calculation of complex flows and to studies of their physical behavior