a source identification problem in a time fractional wave equation with a dynamical boundary condition abstract we focus on a inverse source problem in a partial differential equation containing a fractional derivative in time of the order 1 2 the equation is accompanied with a non standard boundary condition which consists of the classic flux term and the dynamical time fractional derivative term on the one part of the boundary to determine both the solution of the equation and the source term a measurement in a form of a integral over space domain is considered using a time discretization and rothe s method we prove an existence of the strong solution in the suitable functional spaces and the error estimate is established moreover the uniqueness is addressed the results are supported by some numerical experiments

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

meshless implementation of the geometrically exact kirchhoff love shell theory summary in the present paper a meshless generalized multiple fixed least squares implementation of the geometrically exact kirchhoff love shell theory is described the material time derivative of the deformation gradient and the first piola kirchhoff stress tensor are considered as basic conjugate quantities to evaluate the internal power the shell s initial geometry is reproduced exactly by the predefined mapping from a reference plane configuration as a constitutive model a neo hookean material whose functional is altered in compliance with the plane stress condition is chosen the augmented weak form suitable for both interpolative and non interpolative approximations thanks to the imposition of the essential boundary conditions through lagrange multipliers is consistently linearized and the resultant bilinear form proved to be symmetric the appearance of the corner reactions related to the jumps of the pseudo torsion boundary moment requires the inclusion of additional pointwise displacement constraints at the essential boundary corners the importance of these quantities is demonstrated in the numerical tests revealing its positive influence on the displacements and particularly their derivatives up to 3rd order in both linear and nonlinear problems the possibility of incorporation of drilling boundary moment for nonlinear problems was successfully assessed copyright 2014 john wiley sons ltd

an isogeometric reissner mindlin shell element based on bezier dual basis functions overcoming locking and improved coarse mesh accuracy abstract we develop a mixed geometrically nonlinear isogeometric reissner mindlin shell element for the analysis of thin walled structures that leverages bezier dual basis functions to address both shear and membrane locking and to improve the quality of computed stresses the accuracy of computed solutions over coarse meshes that have highly non interpolatory control meshes is achieved through the application of a continuous rotational approach the starting point of the formulation is the modified hellinger reissner variational principle with independent displacement membrane and shear strains as the unknown fields to overcome locking the strain variables are interpolated with lower order spline bases while the variations of the strain variables are interpolated with the corresponding bezier dual bases leveraging the orthogonality property of the bezier dual basis the strain variables are condensed out of the system with only a slight increase in the bandwidth of the resulting linear system the condensed approach preserves the accuracy of the non condensed mixed approach but with fewer degrees of freedom from a practical point of view since the bezier dual basis is completely specified through bezier extraction any spline space that admits bezier extraction can utilize the proposed approach directly

a 4 node finite shell element for the implementation of general hyperelastic 3d elasticity at finite strains abstract in this paper a finite shell element for large deformations is presented based on extensible director kinematics the essential feature is an interface to arbitrary three dimensional material laws the non linear lagrangian formulation is based on the three field variational principle parametrized with the displacement vector enhanced green lagrangian strain tensor and second piola kirchhoff stress tensor the developed quadrilateral shell element is characterized by a course mesh accuracy and distortion insensitivity compared with bilinear displacement approaches furthermore plane stress response is approximately recovered in the asymptotic case of vanishing thickness a number of example problems investigating large deformation as well as finite strain applications are presented compressible and incompressible hyperelastic materials of the st venant kirchhoff neo hookean and mooney rivlin type are particularly used

theory and numerics of layered shells with variationally embedded interlaminar stresses abstract present paper deals with layered shells subjected to static loading the basic equations include besides the global equilibrium formulated in terms of stress resultants the local equilibrium in terms of stresses the geometric field equations the constitutive equations a constraint which enforces the correct shape of the superposed displacement field through the thickness and the boundary conditions thereby an interface to three dimensional material laws is created the weak form of the boundary value problem is derived and a finite element formulation for quadrilaterals is specified the mixed hybrid shell element possesses the usual 5 or 6 nodal degrees of freedom this allows standard geometrical boundary conditions and the elements are applicable also to shell intersection problems for linear elasticity the computed transverse shear stresses are automatically continuous at layer boundaries and zero at the outer surfaces in comparison to fully 3d computations present element formulation needs only a fractional amount of computing time

global existence theory and chaos control of fractional differential equations in this paper the initial value problem for a class of fractional differential equations is discussed which generalizes the existent result to a wide class of fractional differential equations also the theoretical result established in the paper ensures the validity of chaos control of fractional differential equations in particular feed back control of chaotic fractional differential equation is theoretically investigated and the fractional lorenz system as a numerical example is further provided to verify the analytical result

on a stress resultant geometrically exact shell model part vii shell intersections with dof finite element formulations abstract if the mid surface of a shell is smooth the classical theory describes the orientation of the director field attached to the mid surface by two independent rotational degrees of freedom at a shell intersection where this smoothness assumption no longer holds it is shown that the director field in the full nonlinear continuum shell equations must be necessarily described by three degrees of freedom this added degree of freedom however is totally unrelated to the so called drill rotation widely used as a means of tackling the shell intersection problem a computational procedure involving a trivial modification of the global singularity free update procedure described in part iii of this work is described which completely resolves the shell intersection problem without introducing drill springs or related ad hoc devices the proposed approach leaves unchanged standard finite element formulations in terms of 5 dof node affects only the global update formulae and exhibits excellent performance as illustrated by representative numerical simulations

existence and uniqueness of an inverse source problem for a fractional integrodifferential equation abstract we study an inverse source problem for a fractional integrodifferential equation this inverse problem aims to determine a time varying source term in the fractional integrodifferential equation from the measurement data at a fixed point x 0 by using the fixed point theorem in suitable sobolev space the existence and uniqueness of this inverse problem are obtained

fractional wave equation with a frictional memory kernel of mittag leffler type abstract in this paper we give an analytical treatment of a fractional wave equation with caputo time fractional derivative and frictional memory kernel of mittag leffler type this problem generalizes a recently solved problem 62 of a wave equation for a vibrating string in presence of a fractional friction with power law memory kernel such equations can be used in the context of modeling processes in complex and viscoelastic media

a global in time existence and uniqueness result for an integrodifferential hyperbolic inverse problem with memory effect we consider an inverse problem for a one dimensional integrodifferential hyperbolic system which comes from a simplified model of thermoelasticity this inverse problem aims to identify the displacement u the temperature and the memory kernel k simultaneously from the weighted measurement data of temperature by using the fixed point theorem in suitable sobolev spaces the global in time existence and uniqueness results of this inverse problem are obtained moreover we prove that the solution to this inverse problem depends continuously on the noisy data in suitable sobolev spaces for this nonlinear inverse problem our theoretical results guarantee the solvability for the proposed physical model and the well posedness for small measurement time which is quite different from general inverse problems

treatment of reissner mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework this work presents a framework for the computation of complex geometries containing intersections of multiple patches with reissner mindlin shell elements the main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization nor user interaction to quantify the number of rotational degrees of freedom for every node for this purpose the following set of methods is presented control points with corresponding physical location are assigned to one common node for the finite element solution a nodal basis system in every control point is defined which ensures an exact interpolation of the director vector throughout the whole domain a distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented an isogeometric reissner mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches the parametrization of adjacent patches along the interface has to be conforming the shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector the nonlinear kinematic allows the computation of large deformations and large rotations two concepts for the description of rotations are presented the first one uses an interpolation which is commonly used in standard lagrange based shell element formulations the second scheme uses a more elaborate concept proposed by the authors in prior work which increases the accuracy for arbitrary curved geometries numerical examples show the high accuracy and robustness of both concepts the applicability of the proposed framework is demonstrated

four node semi eas element in six field nonlinear theory of shells we propose a new four node c finite element for shell structures undergoing unlimited translations and rotations the considerations concern the general six field theory of shells with asymmetric strain measures in geometrically nonlinear static problems the shell kinematics is of the two dimensional cosserat continuum type and is described by two independent fields the vector field for translations and the proper orthogonal tensor field for rotations all three rotational parameters are treated here as independent hence as a consequence of the shell theory the proposed element has naturally six engineering degrees of freedom at each node with the so called drilling rotation this property makes the element suitable for analysis of shell structures containing folds branches or intersections to avoid locking phenomena we use the enhanced assumed strain eas concept we derive and linearize the modified hu washizu principle for six field theory of shells what makes the present approach original is the combination of eas method with asymmetric membrane strain measures based on literature we propose new enhancing field and specify the transformation matrix that accounts for the lack of symmetry to gain knowledge about the suitability of this field for asymmetric strain measures and to assess the performance of the element we solve typical benchmark examples with smooth geometry and examples involving orthogonal intersections of shell branches

on a solution to fractional order integrodifferential equations with analytic semigroups abstract in this paper we study a class of fractional order integrodifferential equations considered in an arbitrary banach space using the theory of analytic semigroups we establish the existence uniqueness and regularity of a mild solution to these fractional order integrodifferential equations

initial value boundary value problems for fractional diffusion wave equations and applications to some inverse problems abstract we consider initial value boundary value problems for fractional diffusion wave equation t u x t l u x t where 0 2 where l is a symmetric uniformly elliptic operator with t independent smooth coefficients first we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to and the proofs are based on the eigenfunction expansions second for 0 1 we apply the eigenfunction expansions and prove i stability in the backward problem in time ii the uniqueness in determining an initial value and iii the uniqueness of solution by the decay rate as t iv stability in an inverse source problem of determining t dependent factor in the source by observation at one point over 0 t

physical stabilization of the 4 node shell element with one point quadrature abstract a new four node shell element for nonlinear analysis which is useful for explicit time integration with single point quadrature is presented an assumed strain method is used to stabilize the zero energy modes of the element the stabilization procedure is based on the hu washizu variational principle and does not require the input of any stabilization parameters example problems show good accuracy and rate of convergence compared with fully integrated 4 node elements however the physically stabilized element is substantially faster than the fully integrated element

an efficient and robust rotational formulation for isogeometric reissner mindlin shell elements abstract this work is concerned with the development of an efficient and robust isogeometric reissner mindlin shell formulation for the mechanical simulation of thin walled structures such structures are usually defined by non uniform rational b splines nurbs surfaces in industrial design software the usage of isogeometric shell elements can avoid costly conversions from nurbs surfaces to other surface or volume geometry descriptions the shell formulation presented in this contribution uses a continuous orthogonal rotation described by rodrigues tensor in every integration point to compute the current director vector the rotational state is updated in a multiplicative manner large deformations and finite rotations can be described accurately the proposed formulation is robust in terms of stable convergence behavior in the nonlinear equilibrium iteration for large load steps and geometries with large and arbitrary curvature and in terms of insensitivity to shell intersections with kinks under small angles three different integration schemes and their influence on accuracy and computational costs are assessed the efficiency and robustness of the proposed isogeometric shell formulation is shown with the help of several examples accuracy and efficiency is compared to an isogeometric shell formulation with the more common discrete rotational concept and to lagrange based finite element shell formulations the competitiveness of the proposed isogeometric shell formulation in terms of computational costs to attain a pre defined error level is shown

a stabilization procedure for the quadrilateral plate element with one point quadrature a stabilization procedure is developed for controlling the kinematic modes of the four node bilinear quadrilateral element when single point quadrature is used these kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness in this stabilization procedure additional generalized strains are defined which are activated by the kinematic modes these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral by using a scaling law developed in an earlier paper the stabilization parameters are defined so they do not adversely affect the element s performance several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems

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

a mixed shell formulation accounting for thickness strains and finite strain 3d material models a non linear quadrilateral shell element for the analysis of thin structures is presented the reissner mindlin theory with inextensible director vector is used to develop a three field variational formulation with independent displacements stress resultants and shell strains the interpolation of the independent shell strains consists of two parts the first part corresponds to the interpolation of the stress resultants within the second part independent thickness strains are considered this allows incorporation of arbitrary non linear 3d constitutive equations without further modifications the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison with other element formulations we present results for finite strain elasticity inelasticity bifurcation and post buckling problems copyright 2007 john wiley sons ltd

a stabilized one point integrated quadrilateral reissner mindlin plate element a new quadrilateral reissner mindlin plate element with 12 element degrees of freedom is presented for linear isotropic elasticity a hellinger reissner functional with independent displacements rotations and stress resultants is used within the mixed formulation the stress resultants are interpolated using five parameters for the bending moments and four parameters for the shear forces the hybrid element stiffness matrix resulting from the stationary condition can be integrated analytically this leads to a part obtained by one point integration and a stabilization matrix the element possesses a correct rank does not show shear locking and is applicable for the evaluation of displacements and stress resultants within the whole range of thin and thick plates the bending patch test is fulfilled and the computed numerical examples show that the convergence behaviour is better than comparable quadrilateral assumed strain elements copyright 2004 john wiley sons ltd

an energy momentum consistent method for transient simulations with mixed finite elements developed in the framework of geometrically exact shells summary in this paper a mixed variational formulation for the development of energy momentum consistent emc time stepping schemes is proposed the approach accommodates mixed finite elements based on a hu washizu type variational formulation in terms of displacements green lagrangian strains and conjugated stresses the proposed discretization in time of the mixed variational formulation under consideration yields an emc scheme in a natural way the newly developed methodology is applied to a high performance mixed shell finite element the previously observed robustness of the mixed finite element formulation in equilibrium iterations extends to the transient regime because of the emc discretization in time copyright 2016 john wiley sons ltd

multi scale boundary element modelling of material degradation and fracture in the present paper a multi scale boundary element method for modelling damage is proposed the constitutive behaviour of a polycrystalline macro continuum is described by micromechanics simulations using averaging theorems an integral non local approach is employed to avoid the pathological localization of micro damage at the macro scale at the micro scale multiple intergranular crack initiation and propagation under mixed mode failure conditions is considered moreover a non linear frictional contact analysis is employed for modelling the cohesive frictional grain boundary interfaces both micro and macro scales are being modelled with the boundary element method additionally a scheme for coupling the micro bem with a macro fem is also proposed to demonstrate the accuracy of the proposed method the mesh independency is investigated and comparisons with two macro fem models are made to validate the different modelling approaches finally microstructural variability of the macro continuum is considered to investigate possible applications to heterogeneous materials

on a time fractional reaction diffusion equation a reaction diffusion equation with a caputo fractional derivative in time and with various boundary conditions is considered under some conditions on the initial data we show that solutions may experience blow up in a finite time however for realistic initial conditions solutions are global in time moreover the asymptotic behavior of bounded solutions will be analyzed

a finite strain solid shell using local lowdin frames and least squares strains abstract a finite strain solid shell element is proposed it is based on least squares in plane assumed strains assumed natural transverse shear and normal strains the singular value decomposition svd is used to define local integration point orthogonal frames of reference solely from the jacobian matrix the complete finite strain formulation is derived and tested assumed strains obtained from least squares fitting are an alternative to the enhanced assumed strain eas formulations and in contrast with these the result is an element satisfying the patch test there are no additional degrees of freedom as it is the case with the enhanced assumed strain case even by means of static condensation least squares fitting produces invariant finite strain elements which are shear locking free and amenable to be incorporated in large scale codes with that goal we use automatically generated code produced by acegen and mathematica all benchmarks show excellent results similar to the best available shell and hybrid solid elements with significantly lower computational cost

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

on the existence of a global minimum in inverse parameters identification by self optimizing inverse analysis method abstract in this paper a mathematical proof of the existence of a global minimum of self optim self optimizing inverse analysis method cost functional is presented based upon weak solution theory of partial differential equations the self optim provides single global minimum rather than having multiple global minima corresponding to unrealistic solutions of the inverse problem furthermore discrete approximation of the inverse problem and computational methods for the cost functional are proposed and the proof is numerically verified this paper provides a rigorous mathematical foundation for applications of the self optim method to various inverse problems in mechanics

theory and numerics of three dimensional beams with elastoplastic material behaviour a theory of space curved beams with arbitrary cross sections and an associated finite element formulation is presented within the present beam theory the reference point the centroid the centre of shear and the loading point are arbitrary points of the cross section the beam strains are based on a kinematic assumption where torsion warping deformation is included each node of the derived finite element possesses seven degrees of freedom the update of the rotational parameters at the finite element nodes is achieved in an additive way applying the isoparametric concept the kinematic quantities are approximated using lagrangian interpolation functions since the reference curve lies arbitrarily with respect to the centroid the developed element can be used to discretize eccentric stiffener of shells due to the implemented constitutive equations for elastoplastic material behaviour the element can be used to evaluate the load carrying capacity of beam structures copyright 2000 john wiley sons ltd

an inverse source problem for a two parameter anomalous diffusion with local time datum abstract we determine the space dependent source term for a two parameter fractional diffusion problem subject to nonlocal non self adjoint boundary conditions and two local time distinct datum a bi orthogonal pair of bases is used to construct a series representation of the solution and the source term the two local time conditions spare us from measuring the fractional integral initial conditions commonly associated with fractional derivatives on the other hand they lead to delicate 2 2 linear systems for the fourier coefficients of the source term and of the fractional integral of the solution at t 0 the asymptotic behavior and estimates of the generalized mittag leffler function are used to establish the solvability of these linear systems and to obtain sufficient conditions for the existence of our construction analytical and numerical examples are provided

a systematic construction of b bar functions for linear and non linear mixed enhanced finite elements for plane elasticity problems in a previous paper a modified hu washizu variational formulation has been used to derive an accurate four node plane strain stress finite element denoted qe2 for the mixed element qe2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case in this paper an alternative approach is discussed the new formulation leads to the same accuracy for linear elastic problems as the qe2 element however it turns out to be more efficient in numerical simulations especially for large deformation problems using orthogonal stress and strain functions we derive b functions which avoid numerical inversion of matrices the b strain matrix is sparse and has the same structure as the strain matrix b obtained from a compatible displacement field the implementation of the derived mixed element is basically the same as the one for a compatible displacement element the only difference is that we have to compute a b strain matrix instead of the standard b matrix accordingly existing subroutines for a compatible displacement element can be easily changed to obtain the mixed enhanced finite element which yields a higher accuracy than the q4 and qm6 elements copyright 1999 john wiley sons ltd

a robust non linear mixed hybrid quadrilateral shell element in the paper a non linear quadrilateral shell element for the analysis of thin structures is presented the variational formulation is based on a hu washizu functional with independent displacement stress and strain fields the interpolation matrices for the mid surface displacements and rotations as well as for the stress resultants and strains are specified restrictions on the interpolation functions concerning fulfillment of the patch test and stability are derived the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test using newton s method the finite element approximation of the stationary condition is iteratively solved our formulation can accommodate arbitrary non linear material models for finite deformations in the examples we present results for isotropic plasticity at finite rotations and small strains as well as bifurcation problems and post buckling response the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison to other element formulations copyright 2005 john wiley sons ltd

explicit algorithms for the nonlinear dynamics of shells abstract a finite element formulation and algorithm for the nonlinear analysis of the large deflection materially nonlinear response of impulsively loaded shells is presented a unique feature of this algorithm is the use of a bilinear four node quadrilateral element with single point quadrature and a simple hourglass control which is orthogonal to rigid body modes on an element level and does not compromise the consistency of the equations the geometric nonlinearities are treated by using a corotational description wherein a coordinate system that rotates with the material is embedded at the integration point thus the algorithm is directly applicable to anisotropic materials without any corrections for frame invariance of material property tensors this algorithm can treat about 200 element time steps per cpu second on a cyber 170 730 computer in the explicit time integration mode numerous results are presented for both elastic and elastic plastic problems with large strains that show that the method in most cases is comparable in accuracy with an earlier version of this algorithm employing a cubic triangular plate shell element but substantially faster

on shear correction factors in the non linear theory of elastic shells abstract theoretical values of two correction factors s 5 6 and t 7 10 are established for the respective transverse shear stress resultants and stress couples within the general dynamically and kinematically exact six field theory of elastic shells these values do not depend on the shell material symmetry geometry of the base surface the shell thickness or any kind of kinematic and or dynamic constraints the analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section the appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with s and t as the respective correction factors four numerical examples of highly non linear shell structures illustrate the influence of different values of s and t on the results in particular some influence of t is noticed on the placement of bifurcation points in dynamic problem of flight of three intersecting plates analysed with newmark type temporal algorithm the value of t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

a coupled two scale shell model with applications to layered structures summary in this paper a coupled two scale shell model is presented a variational formulation and associated linearization for the coupled global local boundary value problem is derived for small strain problems various numerical solutions are computed within the so called fe 2 method the discretization of the shell is performed with quadrilaterals whereas the local boundary value problems at the integration points of the shell are discretized using 8 noded or 27 noded brick elements or so called solid shell elements at the bottom and top surface of the representative volume element stress boundary conditions are applied whereas at the lateral surfaces the in plane displacements are prescribed for the out of plane displacements link conditions are applied the coupled nonlinear boundary value problems are simultaneously solved within a newton iteration scheme with an important test the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified copyright 2013 john wiley sons ltd

an inverse source problem in a semilinear time fractional diffusion equation we study an inverse source problem for a semilinear time fractional diffusion equation of second order in a bounded domain in r d the missing solely time dependent source is recovered from an additional integral measurement the existence uniqueness and regularity of a weak solution is addressed we design a numerical algorithm based on rothe s method derive a priori estimates and prove convergence of iterates towards the exact solution theoretical results are supported by a numerical experiment

identification of a source in a fractional wave equation from a boundary measurement abstract we deal with an inverse source problem in a time fractional wave equation the time dependent source term is reconstructed using the additional non invasive measurement in the form of integral over a part of the boundary we look for the solution and the source term obeying the variational formulation and the equation obtained from applying the measurement on the equation using the rothe method the existence of the solution is proven the uniqueness is shown in appropriate spaces and some numerical experiments are presented

optimal solid shells for non linear analyses of multilayer composites ii dynamics abstract we are presenting a simple low order solid shell element formulation having only displacement degrees of freedom dofs i e without rotational dofs that has an optimal number of parameters to pass the patch tests and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio with the dynamics referred to a fixed inertial frame the elements can be used to analyze multilayer shell structures undergoing large overall motion the formulation of this element is based on the mixed hu washizu variational principle leading to a novel enhancing strain tensor enhanced assumed strain eas method that renders the computation particularly efficient with improved in plane and out of plane bending behavior poisson thickness locking especially in refined analyses of composite structures involving a large number of high aspect ratio layers the energy momentum conserving algorithm in the context of current solid shell element is presented we discuss the eas formulation based on the displacement gradient and its complexity compared to formulation on the green lagrange strain shear locking and curvature thickness locking are treated using the assumed natural strain ans method the element has an optimal combination of the ans method and the minimal number of eas parameters required to pass the plate bending patch test numerical examples involving dynamic analyses with conservation of energy and momentum of multilayer shell structures having a large range of element aspect ratios are presented several implicit direct integration methods with without numerical dissipation are used and compared in terms of the accuracy stability and cost in multilayer shell structure finally we note that the topic in this paper is a fitting dedication to professor ekkehard ramm who has made important pioneering contributions in this research direction

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

a linear quadrilateral shell element with fast stiffness computation abstract a new quadrilateral shell element with 5 6 nodal degrees of freedom is presented assuming linear isotropic elasticity a hellinger reissner functional with independent displacements rotations and stress resultants is used within the mixed formulation the stress resultants are interpolated using five parameters for the membrane forces as well as for the bending moments and four parameters for the shear forces the hybrid element stiffness matrix resulting from the stationary condition is integrated analytically this leads to a part obtained by one point integration and a stabilization matrix the element possesses the correct rank is free of locking and is applicable within the whole range of thin and thick shells the in plane and bending patch tests are fulfilled and the computed numerical examples show that the convergence behaviour of the stress resultants is very good in comparison to comparable existing elements the essential advantage is the fast stiffness computation due to the analytically integrated matrices

fractional diffusion in inhomogeneous media starting from the continuous time random walk ctrw scheme with the space dependent waiting time probability density function pdf we obtain the time fractional diffusion equation with varying in space fractional order of time derivative as an example we study the evolution of a composite system consisting of two separate regions with different subdiffusion exponents and demonstrate the effects of non trivial drift and subdiffusion whose laws are changed in the course of time

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

maximum principle for the generalized time fractional diffusion equation abstract in the paper a maximum principle for the generalized time fractional diffusion equation over an open bounded domain g 0 t g r n is formulated and proved the proof of the maximum principle is based on an extremum principle for the caputo dzherbashyan fractional derivative that is given in the paper too the maximum principle is then applied to show that the initial boundary value problem for the generalized time fractional diffusion equation possesses at most one classical solution and this solution continuously depends on the initial and boundary conditions

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

analysis of thin shells using anisotropic polyconvex energy densities in this contribution the numerical framework for the simulation of anisotropic thin shells is presented on the basis of polyconvex strain energy functions the nonlinear shell theory is based on the reissner mindlin kinematic along with inextensible director vectors for the variational framework we consider a three field variational functional taking into account independent displacements enhanced strains and stress resultants where the latter field is eliminated by the evaluation of some orthogonality conditions the iterative enforcement of the zero normal stress condition at the integration points allows consideration of arbitrary three dimensional constitutive equations due to the fact that we are interested in fiber reinforced materials we consider an additive structure of the energy decoupled in an isotropic part for the matrix and a superposition of transversely isotropic parts for the fiber families for the representation of the anisotropy we use the concept of structural tensors and formulate the strain energy function in terms of principal and mixed invariants of the right cauchy green tensor and the structural tensor in order to guarantee the existence of minimizers we focus on polyconvex strain energy functions the anisotropy effect is documented in several representative examples

improved four node hellinger reissner elements based on skew coordinates mixed four node elements based on the hellinger reissner hr functional are developed for stress representations in various coordinates including the skew natural and cartesian ones the two field hr functional is used in the classical form and in the incremental form suitable for non linear materials we argue that the skew coordinates not the natural ones should be associated with the natural basis at the element s center if 5 and 7 parameter stress representations are assumed in these coordinates then for a linear elastic case the homogenous equilibrium equations and the stress form of compatibility equation are satisfied point wise two mixed four node elements are developed and tested 1 an assumed stress element hr5 s is developed from the non enhanced hr functional for a 5 parameter representation of stresses formally identical as the one used for example in pian and sumihara int j numer meth engng 1984 20 1685 1695 but in terms of skew coordinates this element is very simple and uses a smaller number of parameters but is equally accurate as the elements by yuan et al int j numer meth engng 1993 36 1747 1763 and by piltner and taylor int j numer meth engng 1995 38 1783 1808 2 an assumed stress enhanced strain element hr9 is developed from the enhanced hr functional for a 7 parameter representation of stress and a 2 parameter enhanced assumed displacement gradient or enhanced assumed strain enhancement various forms of 7 parameter representations appearing in the literature are reviewed and we prove that they are linked by a linear onto transformation the choice of coordinates for the stress and the enhancement turns out to be the crucial factor and four combinations of coordinates for which the element performs the best are identified both elements are based on the green strain and several numerical tests show their good accuracy in particular their robustness to shape distortions for coarse meshes two update schemes for the multipliers of modes and the incremental constitutive procedure accounting for the plane stress condition for non linear materials are tested for large deformation problems copyright 2008 john wiley sons ltd

the weak substitution method an application of the mortar method for patch coupling in nurbs based isogeometric analysis in this contribution a mortar type method for the coupling of non conforming nurbs surface patches is proposed the connection of non conforming patches with shared degrees of freedom requires mutual refinement which propagates throughout the whole patch due to the tensor product structure of nurbs surfaces thus methods to handle non conforming meshes are essential in nurbs based isogeometric analysis the main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation the deformations of the interface control points of adjacent patches are interrelated with a master slave relation this relation is established numerically using the weak form of the equality of mutual deformations along the interface with the help of this relation the interface degrees of freedom of the slave patch can be condensated out of the system a natural connection of the patches is attained without additional terms in the weak form the proposed method is also applicable for nonlinear computations without further measures linear and geometrical nonlinear examples show the high accuracy and robustness of the new method a comparison to reference results and to computations with the lagrange multiplier method is given

stress resultant plasticity for shells revisited in this work we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the ilyushin shapiro two surface yield function with isotropic and kinematic hardening the main focus is on implicit projection algorithms for computation of updated values of internal variables for stress resultant shell elastoplasticity four different algorithms are derived and compared three of them yield practically identical final results yet they differ considerably in computational efficiency and implementation complexity since they solve different sets of equations and they use different procedures that choose active yield surfaces one algorithm does not provide acceptable accuracy it turns out that the most simple and straightforward algorithm performs surprisingly well and efficiently several numerical examples are presented to illustrate the ilyushin shapiro stress resultant shell formulation and the numerical performance of the presented integration algorithms