a locking free fem for cavitation computation in nearly incompressible nonlinear elasticity abstract a reduced selective integration finite element method coupled with a gradient flow method is introduced for the cavitation computation in nearly incompressible nonlinear elasticity numerical experiments show that for the iso parametric biquadratic finite element approximation of the displacement field the method is locking free and efficient for the nearly incompressible cavitation computation and has the same optimal convergence rates as in the compressible case for the elastic energy as well as the deformation and stress field if and only if the reduced integration is applied to the bulk energy term using no more than 2 gaussian quadrature nodes in each dimension

the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

adaptive estimation of the dynamics of a discrete time stochastic volatility model abstract this paper is concerned with the discrete time stochastic volatility model y i exp x i 2 i x i 1 b x i x i i 1 where only y i is observed the model is rewritten as a particular hidden model z i x i e i x i 1 b x i x i i 1 where i and e i are independent sequences of i i d noise moreover the sequences x i and e i are independent and the distribution of e is known then our aim is to estimate the functions b and 2 when only observations z 1 z n are available we propose to estimate b f and b 2 2 f and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces by ratio strategy estimators of b and 2 are then deduced the mean square risk of the resulting estimators are studied and their rates are discussed lastly simulation experiments are provided constants in the penalty functions defining the estimators are calibrated and the quality of the estimators is checked on several examples

generalized mixed variational principles and solutions of ill conditioned problems in computational mechanics part ii shear locking abstract although the finite element method fem has been extensively applied to various areas of engineering the ill conditioned problems occurring in many situations are still thorny to deal with this study attempts to provide a high performing and simple approach to the solutions of ill conditioned problems the theoretical foundation of it is the parametrized variational principles called the generalized mixed variational principles gmvps initiated by rong in 1981 gmvps can solve many kinds of ill conditioned problems in computational mechanics among them four cases are investigated in detail the volumetric locking the shear locking the inhomogeneousness and the membrane locking problems composing four parts of the study part i part iv respectively this paper is part ii wherein a gmvp specially suited to the reissner plate theory and timoshenko beam theory is constructed providing a mathematical foundation for establishing fem formulations which can automatically unlock the shear locking and produce no spurious zero energy modes

optimal model selection for stationary data under various mixing conditions we build penalized least squares estimators of the marginal density of a stationary process using the slope algorithm and resampling penalties when the data are beta or tau mixing these estimators satisfy oracle inequalities with leading constant asymptotically equal to 1

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 method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

finite element analysis of anisotropic non linear incompressible elastic solids by a mixed model a mixed finite element method is presented for geometrically and materially non linear analysis of anisotropic incompressible hyperelastic materials an incremental iteractive total lagrangian formulation is adopted the nodal displacements and the hydrostatic pressure are independently interpolated leading to a mixed system of equations with characteristic zero diagonal terms computations are carried out using a three dimensional linear displacement constant pressure element a mixed penalty approximation is then employed to eliminate the pressure variables at the element level the anisotropic material handling capability of the formulation is tested through a number of transversely isotropic problems and the results compared to analytical solutions to demonstrate the applicability of this formulation to model complex anisotropic problems the inflation of a cut toroidal tube with helical fibre orientation is analysed

a stabilized mixed finite element method for darcy flow we develop new stabilized mixed finite element methods for darcy flow stability and an a priori error estimate in the stability norm are established a wide variety of convergent finite elements present themselves unlike the classical galerkin formulation which requires highly specialized elements an interesting feature of the formulation is that there are no mesh dependent parameters numerical tests confirm the theoretical results 2002 elsevier science b v all rights reserved

limiting spectral distribution of gram matrices associated with functionals of β mixing processes we give asymptotic spectral results for gram matrices of the form n 1 x n x t n where the entries of x n are dependent across both rows and columns and that are functionals of absolutely regular sequences and have only finite second moments we derive under mild dependence conditions in addition to an arithmetical decay condition on the mixing coefficients an integral equation of the stieltjes transform of the limiting spectral distribution of n 1 x n x t n in terms of the spectral density of the underlying process applications to examples of positive recurrent markov chains and dynamical systems are also given

on stress interpolation for hybrid models a technique is proposed for the selection of stress interpolations for hybrid models the present paper applies this approach to plane problems the stiffness matrix is derived using the hellinger reissner variational principle this formulation uses infinitesimal equilibrium relationships and divides the assumed stress into its lower order and higher order parts the patch test can be passed and the resulting elements are generally invariant a plane four node quadrilateral element is described and compared with existing elements numerical studies show that the accuracy of the element is generally good

the development of hybrid axisymmetric elements based on the hellinger reissner variational principle we present a general procedure for the development of hybrid axisymmetric elements based on the hellinger reissner principle within the context of linear elasticity similar to planar elements the stress interpolation is obtained by an identification of the zero energy modes we illustrate our procedure by designing a lower order four node and a higher order nine node element both elements are of correct rank and moreover use the minimum number of stress parameters namely seven and 17 several examples are presented to show the excellent performance of both elements under various demanding situations such as when the material is almost incompressible when the thickness to radius ratio is very small etc when the variation of the field variables is along the radial direction alone when the mesh is uniform and the loading is of pressure type the developed elements are superconvergent i e they yield the exact nodal displacement values

some recent trends and developments in finite element analysis for incompressible thermal flows a numerical procedure for solving the time dependent incompressible navier stokes and energy equations is presented the present method is based on a set of finite element equations of the primitive variable formulation and a time splitting procedure which has unique features in its formulation as well as in its evaluation from the viewpoint of efficiency and accuracy the applicability of the proposed formulation was verified by computations and comparison with known results

optimal structural design considering flexibility a topology optimization method based on the homogenization method the homogenization design method has been successfully applied to a variety of optimization problems such as the stiffness maximization problem and the eigen frequency maximization problem in this study a methodology to obtain the optimal structure design considering flexibility is developed as a new extension of the homogenization design method first flexibility is formulated using the mutual energy concept second a new multi objective function is proposed to obtain optimal solutions incorporating flexibility and stiffness next the topology optimization procedure is constructed using the homogenization method and sequential linear programming slp finally some examples are presented to confirm that the methodology presented here can provide flexible structures satisfying the problem specifications

analysis of mixed finite elements methods for the stokes problem a unified approach we develop a method for the analysis of mixed finite element methods for the stokes problem in the velocity pressure formulation a technical macroelement condition which is sufficient for the classical babuska brezzi inequality to be valid is introduced using this condition we are able to verify the stability and optimal order of convergence of several known mixed finite element methods

rosenthal type inequalities for the maximum of partial sums of stationary processes and examples the aim of this paper is to propose new rosenthal type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations as in the recent results by peligrad et al proc amer math soc 135 2007 541 550 and rio j theoret probab 22 2009 146 163 the estimates of the moments are expressed in terms of the norms of projections of partial sums the proofs of the results are essentially based on a new maximal inequality generalizing the doob maximal inequality for martingales and dyadic induction various applications are also provided

higher order shell elements based on a cosserat model and their use in the topology design of structures for the purpose of carrying out topology optimization of shell structures we show that it is advantageous to use shell elements based on a classical shell theory such as the cosserat theory rather than elements based on the degenerated solid approach since the shell thickness appears explicitly in the formulation thereby greatly simplifying the sensitivity analysis one of the well known shell elements based on the cosserat shell theory is the four node element presented by simo et al comput methods appl mech engrg 72 1989 267 73 1989 53 although one could use this element the use of lower order elements often results in instabilities such as the checkerboard instability in the resulting topologies this provides the motivation for developing higher order shell elements based on a classical shell theory in this work we present the formulation and implementation details for six node and seven node triangular and nine node quadrilateral shell elements which are based on the variational formulation of simo et al and show that good accuracy is obtained even with coarse meshes in fairly demanding problems we also present the topology optimization formulation and some examples of optimal topologies that are obtained using this formulation

natural finite element techniques for viscous fluid motion abstract the paper surveys recent work on fluid dynamics performed at the isd university of stuttgart it is in particular directed to a natural description of the flow phenomena and includes also a consideration of thermally coupled problems the derivation of the relevant finite element equations when referred to natural quantities is outlined and examples of application are given also presented is a discussion on the associated modern developments in numerical solutions techniques

selective and reduced numerical integrations for nurbs based isogeometric analysis we propose a new approach to construct selective and reduced integration rules for isogeometric analysis based on nurbs elements the notion of an approximation space that approximates the target space is introduced we explore the use of various approximation spaces associated with optimal patch wise numerical quadratures that exactly integrate the polynomials in approximation spaces with the minimum number of quadrature points patch rules exploit the higher continuity of spline basis functions the tendency of smooth spline functions to exhibit numerical locking in nearly incompressible problems when using a full gauss legendre quadrature is alleviated with selective or reduced integration stability and accuracy of the schemes are examined analyzing the discrete spectrum in a generalized eigenvalue problem we propose a local algorithm which is robust and computationally efficient to compute element by element the quadrature points and weights in patch rules the performance of the methods is assessed on several numerical examples in two dimensional elasticity and reissner mindlin shell structures

a new efficient approach to the formulation of mixed finite element models for structural analysis abstract a new finite element formulation is developed based on the hellinger reissner principle with independent strain by dividing the assumed strain into the lower order part and the higher order part the new formulation can be made much more efficient than the standard mixed formulation in addition the present new approach provides a rational way of introducing stabilization matrix to suppress undesirable kinematic modes author

optimal convergence properties of the feti domain decomposition method abstract the finite element tearing and interconnecting feti method is a practical and efficient domain decomposition dd algorithm for the solution of self adjoint elliptic partial differential equations for large scale structural problems discretized with shell and beam elements this method was found to outperform popular iterative algorithms and direct solvers on both serial and parallel computers and to compare favorably with leading dd methods in this paper we discuss some numerical properties of the feti method that were not addressed before in particular we show that the mathematical treatment of the floating subdomains and the specific conjugate projected gradient algorithm that characterize the feti method are equivalent to the construction and solution of a coarse problem that propagates the error globally accelerates convergence and ensures a performance that is independent of the number of subdomains we also show that when the interface problem is optimally preconditioned and the mesh is partitioned into well structured subdomains with good aspect ratios the performance of the feti method is also independent of the mesh size however we also argue that the feti and other leading dd methods for unstructured problems lose in practice these scalability properties when the mesh contains junctures with rotational degrees of freedom or the decomposition is irregular and characterized by arbitrary subdomain aspect ratios finally we report that for realistic problems optimal preconditioners are not necessarily computationally efficient and can be outperformed by non optimal ones

copula based time series with filtered nonstationarity abstract economic and financial time series data can exhibit nonstationary and nonlinear patterns simultaneously this paper studies copula based time series models that capture both patterns we introduce a procedure where nonstationarity is removed via a filtration and then the nonlinear temporal dependence in the filtered data is captured via a flexible markov copula we propose two estimators of the copula dependence parameters the parametric two step copula estimator where the marginal distribution of the filtered series is estimated parametrically and the semiparametric two step copula estimator where the marginal distribution is estimated via a rescaled empirical distribution of the filtered series we show that the limiting distribution of the parametric copula estimator depends on the nonstationary filtration and the parametric marginal distribution estimation and may be non normal surprisingly the limiting distribution of the semiparametric copula estimator using the filtered data is shown to be the same as that without nonstationary filtration which is normal and free of marginal distribution specification the simple and robust properties of the semiparametric copula estimators extend to models with misspecified copulas and facilitate statistical inferences such as hypothesis testing and model selection tests on semiparametric copula based dynamic models in the presence of nonstationarity monte carlo studies and real data applications are presented

reduced bezier element quadrature rules for quadratic and cubic splines in isogeometric analysis abstract we explore the use of various element based reduced quadrature strategies for bivariate and trivariate quadratic and cubic spline elements used in isogeometric analysis the rules studied encompass tensor product gauss and gauss lobatto rules and certain so called monomial rules that do no possess a tensor product structure the objective of the study is to determine quadrature strategies which enjoy the same accuracy and stability behavior as full gauss quadrature but with significantly fewer quadrature points several cases emerge that satisfy this objective and also demonstrate superior efficiency compared with standard c 0 continuous finite elements of the same order

finite element hourglassing control a new hourglassing control technique for quadrilateral and hexahedral elements used in dynamic finite element codes is presented based on expansion of the strees in a taylor series and retention of additional terms beyond the usual constant stress term this technique has the advantage that actual rather than artificial material properties are used simplifications that render this technique competitive with artificial viscosity and stiffness procedures in terms of additional storage and computation requirements are described

extrapolated fields in the formulation of the assumed strain elements part ii three dimensional problems abstract a new assumed strain quadrilateral element with accurate in plane bending behavior is presented the basic idea consists in introduction of a parallelogram domain associated with the given quadrilateral element development of the related assumed strain field for the parallelogram and subsequent extrapolation of this field to the domain of the original quadrilateral the assumed strain field for the parallelogram is constructed by identification of various modes of its deformation and then by proper modification of the strain field in some of these modes in particular the strain operator with respect to the so called in plane bending modes is modified so as to simulate the strain field resulting from the assumptions usually made in structural mechanics the modification of the strain fields leads to the assumed strain operator the proposed new assumed strain quadrilateral element exhibits remarkably accurate performance for both membrane and bending dominated problems even when severely distorted and high aspect ratio meshes are considered and when materials are nearly incompressible

a locking free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of lagrangian elements abstract this paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear lagrangian elements it solves the primal variable displacement in the strain div formulation and can handle both displacement and traction boundary conditions it is a locking free solver based on conforming finite elements the solver has second order accuracy in displacement and first order accuracy in stress and dilation divergence of displacement as validated by theoretical analysis and illustrated by numerical experiments on benchmarks deal ii implementation is also discussed

locking spurious mechanisms and pressure divergence in penalty finite element methods for stokes flow problems abstract solution locking spurious mechanisms and pressure divergence exhibited in the stokes flow calculations by the penalty finite element methods are analyzed employing a fourier analysis technique comparison of the approximate discrete operator components with the corresponding continuum ones enables one to explicitly identify the conditions for avoiding locking spurious mechanisms and pressure divergence in terms of discrete operator components which are applicable to either the finite difference or finite element discretizations a synthesis approach is explored to eliminate the solution locking spurious mechanisms and pressure divergence in uniformly reduced integrated four noded elements extensions of the present analysis and synthesis approach to navier stokes equations appear to be straightforward if one deals with a set of consistently linearized operators

a new efficient mixed formulation for thin shell finite element models abstract a nine node shell element is developed by a new and more efficient mixed formulation the new shell element formulation is based on the hellinger reissner principle with independent strain and the concept of degenerate solid shell the new formulation is made more efficient in terms of computing time than the conventional mixed formulation by dividing the assumed strain fields into a lower part and a higher order part numerical results demonstrate that the present nine node element is free of locking even for very thin plates and shells and is also kinematically stable in fact the stiffness matrix associated with the higher order assumed strain plays the role of a stabilization matrix

large deformation triangular and tetrahedral element formulations for unstructured meshes abstract the increasing use of automatic mesh generators and remeshers has spurred the need for accurate and efficient triangular and tetrahedral elements in unstructured meshes in large deformation analysis of solids accuracy and efficiency require the treatment of volumetric locking and element distortions respectively in this paper a mixed formulations is proposed to treat these issues and applied to triangular and tetrahedral elements the formulations enforces in the weak sense the expression for the volumetric strain in terms of the deformation gradient the mixed formulation is combined with an irreducible formulation to provide a balance between the treatment of volumetric locking and the maintenance of an adequate critical timestep three techniques are proposed to determine such a balance at the local element level example computations in two and three dimensions of an iron cylinder impacting a rigid surface are used to demonstrate the formulations and to compare them to the irreducible displacement based formulation

elimination of spurious pressure and kinematic modes in biquadratic nine node plane element in two dimensional penalty finite element analysis of incompressible materials q9 3p the 9 node quadrilateral with three assumed quasi pressure modes is the most popular element not bothered by spurious pressure in constructing the penalty matrix of q9 3p it is necessary to form a 3 18 matrix and a 3 3 symmetric matrix the inverse of the symmetric matrix is then post and pre multiplied by the 3 18 matrix and its transpose respectively by employing a rank subtraction technique a new and more efficient implementation scheme is devised for the penalty matrix same as the conventional q9 element when q9 3p is fully integrated it becomes expensive and too stiff on the other hand there are two spurious kinematic modes should the element be sub integrated in the proposed q9 3p element the two mechanisms will be annihilated by judiciously chosen higher order assumed stress modes in conjunction with a modified hellinger reissner functional it will be demonstrated that the element is of good accuracy and high efficiency

treatment of internal constraints by mixed finite element methods unification of concepts a general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented the assumed fields are constructed in such a way that internal constraints are satisfied a priori consequently the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided to this end the assumed stress and strain fields are constructed to satisfy a priori the homogeneous part of the equilibrium equations thus avoiding fraeijs de veubeke s limitation principle results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated

on the convergence of the bilinear velocity constant pressure finite element method in viscous flow abstract in this paper we show that the standard isoparametric q 1 q 0 velocity pressure finite element method for solving viscous flow problems leads to a fully and optimally convergent sequence of approximations if an appropriate quadrangulation of the domain is used

an integration scheme for prandtl reuss elastoplastic constitutive equations we investigate the generalized midpoint rule for the time integration of elastoplastic constitutive equations for pressure independent yield criteria the incremental equations are divided into one scalar hydrostatic pressure dilation rate equation and a stress deviator strain rate deviator tensorial equation this formulation is applied to two classical problems bulging of a tube under internal pressure and tension test on a notched specimen

a finite element formulation with stabilization matrix for geometrically non linear shells an assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically non linear problems of isotropic and laminated composite shells the present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement the assumed independent strain field is divided into a lower order part and a higher order part subsequently the lower order part is set equal to the displacement dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix the strains and the determinant of the jacobian matrix are assumed to vary linearly in the thickness direction this assumption allows analytical integration through thickness independent of the number of plies a nine node element with a judiciously chosen set of higher order assumed strain field is developed numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formulation

a new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems abstract in order to accurately model the behaviour of geostructures it is usually not possible to neglect the interaction between the soil skeleton and the pore fluid classical finite element models taking into account this interaction are formulated in terms of the displacement and pore pressure fields and are based on the assumption that the fluid acceleration relative to the soil skeleton is negligible this type of mixed problems is similar to others found in solid and fluid mechanics and might give rise to numerical instabilities unless certain requirements are met there are two classical approaches to this problem the first is usually known as the zienkiewicz taylor patch test for mixed formulations as a consequence of this test the interpolation degree of the displacement field is required to be higher than the corresponding one of the pressure field mathematically speaking this is a necessary condition for stability the second approach mathematically more involved is usually known as the bab ska brezzi inf sup condition and constitutes a sufficient condition for stability however it is possible to obtain stable formulations circumventing the interpolation degree requirement through the so called stabilization techniques these techniques were initially applied in the context of fluid mechanics and later extended to solid mechanics this article presents a new formulation in which stabilization is achieved through an approach based on the simo rifai enhanced strain element

two higher order shell finite elements with stabilization matrix a 32 node three dimensional solid element and a 16 node degenerate solid element that are applicable to analysis of thin shell structural problems are presented in this paper both elements are formulated by using the hellinger reissner principle with independent strain the assumed independent strain field is divided into higherand lower order polynomial terms the element stiffness matrix associated with the higher order assumed strain plays the role of the stabilization matrix various types of the higher order assumed strain are tested for the present elements the resulting finite element models require much less time to compute the element stiffness matrix than the corresponding conventional mixed models or assumed displacement models with a full gaussian quadrature rule numerical results demonstrate that with a properly chosen set of higher order assumed strain the present elements produce reliable and very accurate solutions even for very thin plates and thin shells with deeply curved geometry

on the incompressible constraint of the 4 node quadrilateral element the standard plane 4 node element is written as the summation of a constant gradient matrix usually obtained from underintegration and a stabilization matrix the split is based on a taylor series expansion of element basis functions in the incompressible limit the locking effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher order term in the taylor series the incompressibility condition is formulated in a weak sense so that the element displacement field is divergence free when integrated over the element volume the resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first order terms of the taylor series the corresponding eigenvalue enforces incompressibility implicitly by means of a penalty constraint analytical expressions for that constant dilatation eigenpair are derived for arbitrary element geometries it is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner for several classical and recent elements the eigensystems are analysed numerically it is shown that most of the formulations reflect the incompressible constraint identically in the incompressible limit the numerical accuracies of the elements are compared

an interface strip preconditioner for domain decomposition methods application to hydrology in this paper the efficiency of a parallelizable preconditioner for domain decomposition methods in the context of the solution of non symmetric linear equations arising from discretization of the saint venant equations is investigated the proposed interface strip preconditioner is is based on solving a problem in a narrow strip around the interface it requires much less memory and computing time than classical neumann neumann preconditioner and handles correctly the flux splitting among sub domains that share the interface the performance of this preconditioner is assessed with an analytical study of schur complement matrix eigenvalues and numerical experiments conducted in a parallel computational environment consisting of a beowulf cluster of 20 nodes copyright 2005 john wiley sons ltd

an explicit hybrid stabilized 9 node lagrangian shell element abstract this paper presents an explicit hybrid stabilized 9 node lagrangian shell element in the formulation the stress modes pertinent to the stabilization are contravariant in nature and their products with the displacement derived covariant strain are explicit linear functions of the nodal geometric parameters the element is particularly efficient because the leverage matrix or the stabilization vectors can be constructed without resorting to numerical integration or the gram schmidt orthogonalization accuracy of the element is promising and comparable to the state of the art stabilized and hybrid elements

a reduced order representation of the poincare steklov operator an application to coupled multi physics problems this work investigates a model reduction method applied to coupled multi physics systems the case in which a system of interest interacts with an external system is considered an approximation of the poinste operator is computed by simulating in an offline phase the external problem when the inputs are the laplace beltrami eigenfunctions defined at the interface in the online phase only the reduced representation of the operator is needed to account for the influence of the external problem on the main system an online basis enrichment is proposed in order to guarantee a precise reduced order computation several test cases are proposed on different fluid structure couplings

on c0 beam elements with shear and their corresponding penalty function formulation abstract on a model of clamped beam problem we study a finite element method with approximate constraints and the corresponding penalty function approach by a small perturbation analysis we show that the rotation is independent from the penalization this method allows us to use simple c0 elements hence we can compute approximate solutions to obstacle problems the one dimensional nature of all the results is underlined and the extension of this fem to flexible pipe lines is indicated

convergence of mixed finite element approximations for the shallow arch problem the stability and convergence of mixed finite element methods are investigated for an equilibrium problem for thin shallow elastic arches the problem in its standard form contains two terms corresponding to the contributions from the shear and axial strains with a small parameter lagrange multipliers are introduced to formulate the problem in an alternative mixed form questions of existence and uniqueness of solutions to the standard and mixed problems are addressed it is shown that finite element approximations of the mixed problem are stable and convergent reduced integration formulations are equivalent to a mixed formulation which in general is distinct from the formulation shown to be stable and convergent except when the order of polynomial interpolationt of the arch shape satisfies 1 t min 2 r wherer is the order of polynomial approximation of the unknown variables

multiple quadrature underintegrated finite elements new multiple quadrature point underintegrated finite elements with hourglass control are developed the elements are selectively underintegrated to avoid volumetric and shear locking and save computational time an approach for hourglass control is proposed such that the stabilization operators are obtained simply by taking the partial derivatives of the generalized strain rate vector with respect to the natural co ordinates so that the elements require no stabilization parameter to improve accuracy over the traditional one point quadrature elements several quadrature points are used to integrate the internal forces especially for tracing the plastic fronts in the mesh during loading and unloading in elastic plastic analysis two and four point quadrature elements are proposed for use in the two and three dimensional elements respectively other multiple quadrature points can also be employed several numerical examples such as thin beam plate and shell problems are presented to demonstrate the applicability of the proposed elements

remarks on 4cst elements for incompressible materials abstract three node triangular elements obtained from the intersecting diagonals of quadrilaterals are thoroughly investigated for the penalty method formulation of incompressible problems such as stokes flow navier stokes flow and small deformation rubber elasticity equivalence of the present formulation to the one using 4 node quadrilateral isoparametric elements with selective reduced integration is presented convergence instability phenomenon smoothing of the pressure distribution are studied together with decompositions into triangular elements

finite element analysis of linear and non linear planar deformations of elastic initially curved beams reference epfl article 102719view record in web of science record created on 2007 04 23 modified on 2016 08 08

behaviour of isoparametric quadrilateral family of lagrangian fluid finite elements this paper presents the formulation of both the consistent and inconsistent four eight and nine noded isoparametric quadrilateral fluid finite elements that are based on lagrangian frame of reference the mesh locking phenomenon due to simultaneous enforcement of twin constraints namely the incompressibility and irrotationality constraints is studied in detail the study shows that the characteristic of the locked fluid elements is that it always generates numerous spurious acoustic volume change modes upon the enforcement of rotational constraints that is the rotational constraints change the character of certain volume change modes the study further reinforces the necessity of rotational constraints in not only identifying the spurious pressure modes but also in reducing the computational effort for determining the eigenvalues and eigenvectors it is found that all fully integrated inconsistent models exhibit locking behaviour however the inconsistent eight and nine noded elements integrated with full integration of volumetric stiffness and one point integration of the rotational stiffness matrices gives excellent performance although they do not pass the inf sup test the four and nine noded consistent models are found to give locking free performance while their eight noded counterpart exhibited locking behaviour the study shows that only consistent nine noded element models pass the inf sup test the utility of these elements in coupled fluid structure interaction problem is also demonstrated

on a systematic development of trilinear three dimensional solid elements based on simo s enhanced strain formulation a systematic development of eight node trilinear three dimensional solid elements based on simo s theoretical framework for the enhanced assumed strain formulation is presented for linear elasticity the starting point is a regular brick followed by parallelepipeds and then arbitrarily distorted elements the advantages and deficits of various enhanced strain formulations are extensively discussed using the regular brick for arbitrarily distorted elements a simple modification of the element stiffness matrix is proposed to achieve a more reliable and very efficient element on some numerical examples the advantages and limits of the family of enhanced strain elements and the improved elements are discussed

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

inequalities for absolutely regular sequences application to density estimation this paper investigates the problem of density estimation for absolutely regular observations in a first part we state two important results a new variance inequality and a rosenthal type inequality this allows us to study the p integrated risk p 2 of a large class of density estimators including kernel or projection estimators under the summability condition on the mixing coefficients k 0 k 1 p 2 k the rates obtained are those known to be optimal in the independent setting

the two level feti method for static and dynamic plate problems part i an optimal iterative solver for biharmonic systems abstract we present a lagrange multiplier based substructuring method for solving iteratively large scale systems of equations arising from the finite element discretization of static and dynamic plate bending problems the proposed method is essentially an extension of the feti domain decomposition algorithm to fourth order problems the main idea is to enforce exactly the continuity of the transverse displacement field at the substructure corners throughout the preconditioned conjugate projected gradient iterations this results in a two level feti substructuring method where the condition number of the preconditioned interface problem does not grow with the number of substructures and grows at most polylogarithmically with the number of elements per substructure these theoretically proven optimal convergence properties of the new feti method are numerically demonstrated for several finite element plate bending static and transient problems the two level iterative solver presented in this paper is applicable to a large family of biharmonic time independent as well as time dependent systems it is also extendible to shell problems

a general methodology for deriving shear constrained reissner mindlin plate elements in this paper the necessary requirements for the good behaviour of shear constrained reissner mindlin plate elements for thick and thin plate situations are re interpreted and a simple explicit form of the substitute shear strain matrix is obtained this extends the previous work of the authors presented in references 18 and 31 the general methodology is applied to the re formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features some examples of the good behaviour of these elements are given

an analysis of some higher order triangular elements and their susceptibility to hourglassing in lagrangian fluid simulations in lagrangian codes two of the main problems are hourglassing with bilinear quadrilateral elements and mesh locking with linear triangular elements higher order triangular elements with their greater number of degrees of freedom should not suffer from mesh locking hourglassing though is caused by the interaction of the element and the quadrature used to evaluate the integrals of the derivatives on it higher order triangular elements as we shall see unlike their linear counterparts also suffer from this spurious mode a higher order element quadrature combination is found that does not suffer from hourglassing the main fault of this combination is the extra cost involved over the more usual linear or bilinear element with centroid quadrature combination a short discussion is given regarding this point

the b bar method and the limitation principles abstract the generalized elastic material provides a reference model to cast in a unitary framework many structural models which are based on nonlinear monotone multivalued relations such as viscoelasticity plasticity and unilateral models the modified forms of the hu washizu and hellinger reissner principles and the displacement based variational formulation are recovered for the generalized elastic material starting from a functional in the complete set of state variables the related limitation principles are derived and their specialization to elasticity and elastoplasticity with mixed hardening are provided it is shown that the interpolating fields for the pressure and the volumetric strain usually adopted in the b bar method lead to a limitation principle accordingly the same elastic and elastoplastic solutions can be obtained by means of an approximate mixed displacement pressure variational principle a second application is concerned with the conditions ensuring the coincidence of the solutions between an approximate two field mixed formulation and the displacement based method numerical examples are provided to show the coincidence of the solutions obtained from different mixed finite element formulations in elasticity or elastoplasticity under the validity of the limitation principles

feti dp a dual primal unified feti method part i a faster alternative to the two level feti method the feti method and its two level extension feti 2 are two numerically scalable domain decomposition methods with lagrange multipliers for the iterative solution of second order solid mechanics and fourth order beam plate and shell structural problems respectively the feti 2 method distinguishes itself from the basic or one level feti method by a second set of lagrange multipliers that are introduced at the subdomain cross points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations in this paper we present a dual primal formulation of the feti 2 concept that eliminates the need for that second set of lagrange multipliers and unifies all previously developed one level and two level feti algorithms into a single dual primal feti dp method we show that this new feti dp method is numerically scalable for both second order and fourth order problems we also show that it is more robust and more computationally efficient than existing feti solvers particularly when the number of subdomains and or processors is very large copyright 2001 john wiley sons ltd

enhanced linear triangle for plasticity problems in j 2 solids due to their economy and capability to reproduce high gradient zones low order elements are of great interest in the calculations involving localized failure however the performance of the simplest element the three nodes triangle under incompressible and bending dominated situations is very poor and the computed results unreliable this paper presents an inexpensive three fields u p formulation solving these issues as shown in the examples of application

processus empiriques absolument reguliers et entropie universelle nous etendons le theoreme limite central fonctionnel de pollard pour les processus empiriques indexes par des familles de fonctions d entropie universelle integrable aux suites d observations absolument regulieres et stationnaires sous des conditions d entropie universelles sur raisonnables nous montrons un theoreme limite central uniforme pour les suites de variables aleatoires absolument regulieres et stationnaires sous la condition minimale de sommabilite des coefficients de melange n n

adaptive estimation in autoregression or mixing regression via model selection we study the problem of estimatingsome unknown regression function in a beta mixing dependent framework to this end we consider some collection of models which are finite dimensional spaces a penalized least squares estimator plse is built on a data driven selected model among this collection we state non asymptotic risk bounds for this plse and give several examples where the procedure can be applied autoregression regression with arithmetically beta mixing design points regression with mixing errors estimation in additive frameworks estimation of the order of the autoregression in addition we show that under a weak moment condition on the errors our estimator is adaptive in the minimax sense simultaneously over some family of besov balls

c0 finite element discretization of kirchhoff s equations of thin plate bending an alternative formulation of kirchhoff s equations is given which is amenable to a standard c 0 finite element discretization in this formulation the potential energy of the plate is formulated entirely in terms of rotations whereas the deflections are the outcome of a subsidiary problem the nature of the resulting equations is such that c 0 interpolation can be used on both rotations and deflections in particular general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method unlike other finite element methods which are based on three dimensional or mindlin formulations the present approach deals directly with kirchhoff s equations of thin plate bending excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns

finite element solution of the unsteady navier stokes equations by a fractional step method abstract a finite element method is presented for the numerical simulation of time dependent incompressible viscous flows the method is based on a fractional step approach to the time integration of the navier stokes equations in which only the incompressibility condition is treated implicitly this leads to a computational scheme of extremely simple algorithmic structure that is particularly attractive for cost effective solutions of large scale problems numerical results indicate the versatility and effectiveness of the proposed method

new dependence coefficients examples and applications to statistics to measure the dependence between a real valued random variable x and a algebra we consider four distances between the conditional distribution function of x given and the distribution function of x the coefficients obtained are weaker than the corresponding mixing coefficients and may be computed in many situations in particular we show that they are well adapted to functions of mixing sequences iterated random functions and dynamical systems starting from a new covariance inequality we study the mean integrated square error for estimating the unknown marginal density of a stationary sequence we obtain optimal rates for kernel estimators as well as projection estimators on a well localized basis under a minimal condition on the coefficients using recent results we show that our coefficients may be also used to obtain various exponential inequalities a concentration inequality for lipschitz functions and a berry esseen type inequality

optimal spectral approximation of 2n order differential operators by mixed isogeometric analysis abstract we approximate the spectra of a class of 2 n order differential operators using isogeometric analysis in mixed formulations this class includes a wide range of differential operators such as those arising in elliptic biharmonic cahn hilliard swift hohenberg and phase field crystal equations the spectra of the differential operators are approximated by solving differential eigenvalue problems in mixed formulations which require auxiliary parameters the mixed isogeometric formulation when applying classical quadrature rules leads to an eigenvalue error convergence of order 2 p where p is the order of the underlying b spline space we improve this order to be 2 p 2 by applying optimally blended quadrature rules developed in puzyrev et al 2017 caloet al 0000 and this order is an optimum in the view of dispersion error we also compare these results with the mixed finite elements and show numerically that the mixed isogeometric analysis leads to significantly better spectral approximations

continuous discontinuous finite element approximations of fourth order elliptic problems in structural and continuum mechanics with applications to thin beams and plates and strain gradient elasticity abstract a new finite element method for fourth order elliptic partial differential equations is presented and applied to thin bending theory problems in structural mechanics and to a strain gradient theory problem the method combines concepts from the continuous galerkin cg method the discontinuous galerkin dg method and stabilization techniques a brief review of the cg method the dg method and stabilization techniques highlights the advantages and disadvantages of these methods and suggests a new approach for the solution of fourth order elliptic problems a continuous discontinuous galerkin c dg method is proposed which uses c 0 continuous interpolation functions and is formulated in the primary variable only the advantage of this formulation over a more traditional mixed approach is that the introduction of additional unknowns and related difficulties can be avoided in the context of thin bending theory the c dg method leads to a formulation where displacements are the only degrees of freedom and no rotational degrees of freedom need to be considered the main feature of the c dg method is the weak enforcement of continuity of first and higher order derivatives through stabilizing terms on interior boundaries consistency stability and convergence of the method are shown analytically numerical experiments verify the theoretical results and applications are presented for bernoulli euler beam bending poisson kirchhoff plate bending and a shear layer problem using toupin mindlin strain gradient theory

accuracy of some finite element models for arch problems abstract this paper presents a theoretical accuracy study of some finite element models for thin arches as is well known the selection of finite elements for curved members is quite a delicate problem we obtain order estimates of errors of finite element solutions by means of the perturbation theory of mixed models and the technique of asymptotic expansion in particular we theoretically show that certain finite element models may suffer from the so called locking phenomenon numerical results are also given to be compared with the theoretical error estimates

unlocking with residual free bubbles residual free bubbles are derived for the timoshenko beam problem eliminating these bubbles the resulting formulation is form identical in using the following tricks to the standard variational formulation i one point reduced integration on the shear energy term ii replace its coefficient 1 2 by 1 2 hk212 in each element iii modify consistently the right hand side this final formulation is legally obtained in that the galerkin method enriched with residual free bubbles is developed using full integration throughout furthermore this method is nodally exact by construction

a minimal element distortion strategy for computational mesh dynamics mesh motion strategy is one of the key points in many fluid structure interaction fsi problems due to the increasing application of fsi to solve the current challenging engineering problems this topic has become of great interest there are several different strategies to solve this problem some of them use a discrete and lumped spring mass system to propagate the boundary motion into the volume mesh and many others use an elastostatic problem to deform the mesh in all these strategies there is always risk of producing an invalid mesh i e a mesh with some elements inverted normally this condition is irreversible and once an invalid mesh is obtained it is difficult to continue in this paper the mesh motion strategy is defined as an optimization problem by its definition this strategy can be classified as a particular case of an elastostatic problem where the material constitutive law is defined in terms of the minimization of certain energy functional that takes into account the degree of element distortion some advantages of this strategy are its natural tendency to high quality meshes its robustness and its straightforward extension to 3d problems several examples included in this paper show these capabilities even though this strategy seems to be very robust it is not able to recover a valid mesh starting from an invalid one this improvement is left for future work copyright 2006 john wiley sons ltd

control of spurious modes in the nine node quadrilateral element the nine node quadrilateral is much more accurate than its eight node relative if elements are non rectangular however the nine node element may display spurious low energy modes under 2 2 gauss quadrature these modes can be controlled by using the 3 3 quadrature rule but at added cost this paper investigates two inexpensive control devices that can be used with 2 2 gauss quadrature

mixed models and reduced selective integration displacement models for nonlinear analysis of curved beams simple mixed models are developed for the geometrically nonlinear analysis of deep arches a total lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included the fundamental unknowns consist of the six internal forces and generalized displacements of the arch and the element characteristic arrays are obtained by using hellinger reissner mixed variational principle the polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements and the forces are discontinuous at the interelement boundaries the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and compare their performance with other mixed models reported in the literature

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

mixed finite element with drilling rotations for plane problems in finite elasticity abstract in this work we apply the mixed finite element method to construct a two dimensional membrane element with drilling rotations for geometrically nonlinear elasticity only the 4 node element interpolation is discussed but the formulation is plausible for higher order elements as well numerical examples for both linear and nonlinear analyses demonstrate that the element yields rather stiff but indeed convergent results

a bernstein type inequality and moderate deviations for weakly dependent sequences in this paper we present a bernstein type tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that is not necessarily bounded the class considered includes geometrically and subgeometrically strongly mixing sequences the result is then used to derive asymptotic moderate deviation results applications are given for classes of markov chains iterated lipschitz models and functions of linear processes with absolutely regular innovations

analysis of some mixed elements for the stokes problem abstract in this paper we discuss some mixed finite element methods related to the reduced integration penalty method for solving the stokes problem we prove optimal order error estimates for bilinear constant and biquadratic bilinear velocity pressure finite element solutions the result for the biquadratic bilinear element is new while that for the bilinear constant element improves the convergence analysis of johnson and pitkaranta 1982 in the degenerate case when the penalty parameter is set to be zero our results reduce to some related known results proved in by brezzi and fortin 1991 for the bilinear constant element and bercovier and pironneau 1979 for the biquadratic bilinear element our theoretical results are consistent with the numerical results reported by carey and krishnan 1982 and oden et al 1982

hybrid hexahedral element for solids plates shells and beams by selective scaling a robust two field hexahedral element capable of handling plate shell beam and nearly incompressible material analyses without locking are presented starting with the assumed stress element of pian and tong 7 parasitic strain components leading to locking in plate shell and beam analyses are first identified locking can be alleviated by scaling down selectively the parasitic strain components in the leverage matrix unfortunately the element then fails the patch test however patch test correction and reduction in computation can be achieved by the recently proposed admissible matrix formulation the resulting element is lock free and very efficient all matrices involved in constructing the stiffness matrix can be derived explicitly the accuracy of the element is tested by popular bench mark problems