A boundary element procedure for contact problems in plane linear elastostatics
A formulation of Stokes's problem and the linear elasticity equations suggested by the Oldroyd model for viscoelastic flow
A general homogenization result of spectral problem for linearized elasticity in perforated domains
The goal of this paper is to establish a general homogenization result for linearized elasticity of an eigenvalue problem defined over perforated domains, beyond the periodic setting, within the framework of the -convergence theory. Our main homogenization result states that the knowledge of the fourth-order tensor , the -limit of , is sufficient to determine the homogenized eigenvalue problem and preserve the structure of the spectrum. This theorem is proved essentially by using Tartar’s method...
A Generalization of the Schwarz Alternating Method to an Arbitrary Number of Subdomains.
A mimetic discretization method for linear elasticity
A Mimetic Discretization method for the linear elasticity problem in mixed weakly symmetric form is developed. The scheme is shown to converge linearly in the mesh size, independently of the incompressibility parameter λ, provided the discrete scalar product satisfies two given conditions. Finally, a family of algebraic scalar products which respect the above conditions is detailed.
A new method of solving the basic plane boundary value problems of statics of the elastic mixture theory.
A note on the Danilovskaia's problem.
A priori error analysis of a fully-mixed finite element method for a two-dimensional fluid-solid interaction problem
We introduce and analyze a fully-mixed finite element method for a fluid-solid interaction problem in 2D. The model consists of an elastic body which is subject to a given incident wave that travels in the fluid surrounding it. Actually, the fluid is supposed to occupy an annular region, and hence a Robin boundary condition imitating the behavior of the scattered field at infinity is imposed on its exterior boundary, which is located far from the obstacle. The media are governed by the elastodynamic...
A property of the -convergence for elasticity in perforated domains.
A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity
In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities...
A residual based A POSTERIORI error estimator for an augmented mixed finite element method in linear elasticity
In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities...
A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations
We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed...
About the Lamé system in a polygonal or a polyhedral domain and a coupled problem between the Lamé system and the plate equation. II : exact controllability
Algebraic domain decomposition solver for linear elasticity
We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn’s constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.
An augmented mixed finite element method for linear elasticity with non-homogeneous Dirichlet conditions.
Analogues of the Kolosov-Muskhelishvili general representation formulas and Cauchy-Riemann conditions in the theory of elastic mixtures.
Analysis of a new augmented mixed finite element method for linear elasticity allowing -- approximations
We present a new stabilized mixed finite element method for the linear elasticity problem in . The approach is based on the introduction of Galerkin least-squares terms arising from the constitutive and equilibrium equations, and from the relation defining the rotation in terms of the displacement. We show that the resulting augmented variational formulation and the associated Galerkin scheme are well posed, and that the latter becomes locking-free and asymptotically locking-free for Dirichlet...
Analysis of optimality conditions for some topology optimization problems in elasticity
The subject of topology optimization has undergone an enormous practical development since the appearance of the paper by Bendso e and Kikuchi (1988), where some ideas from homogenization theory were put into practice. Since then, several engineering applications as well as different approaches have been developed successfully. However, it is difficult to find in the literature some analytical examples that might be used as a test in order to assess the validity of the solutions obtained with different...
Application of analogues of general Kolosov-Muskhelishvili representations in the theory of elastic mixtures.
Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution
The paper presents the analysis, approximation and numerical realization of 3D contact problems for an elastic body unilaterally supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model (a slip bound is given a priori) but with a coefficient of friction which depends on a solution. It is shown that a solution exists for a large class of and is unique provided that is Lipschitz continuous with a sufficiently small modulus of...