An augmented mixed finite element method for linear elasticity with non-homogeneous Dirichlet conditions.
An elasto-plastic contact problem
An energy-preserving Discrete Element Method for elastodynamics∗
We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration scheme allows us to recover conservation of energy, and thus stability over long time simulations. These theoretical...
An energy-preserving Discrete Element Method for elastodynamics∗
We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration scheme allows us to recover conservation of energy, and thus stability over long time simulations. These theoretical...
An equilibrium finite element method in three-dimensional elasticity
The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates in -norm and in -norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too.
An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure
In this note we give sharp lower bounds for a non-convex functional when minimised over the space of functions that are piecewise affine on a triangular grid and satisfy an affine boundary condition in the second lamination convex hull of the wells of the functional.
An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure
In this note we give sharp lower bounds for a non-convex functional when minimised over the space of functions that are piecewise affine on a triangular grid and satisfy an affine boundary condition in the second lamination convex hull of the wells of the functional.
Analyse numérique d'un modèle de coques de Koiter discrétisé en base cartésienne par éléments finis DKT
Analysis and Numerical Approximation of an Electro-elastic Frictional Contact Problem
We consider the problem of frictional contact between an piezoelectric body and a conductive foundation. The electro-elastic constitutive law is assumed to be nonlinear and the contact is modelled with the Signorini condition, nonlocal Coulomb friction law and a regularized electrical conductivity condition. The existence of a unique weak solution of the model is established. The finite elements approximation for the problem is presented, and error...
Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem
A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables. Spectral...
Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem
A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables....
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 Finite Element Methods for the Nonlinear Dynamic Analysis of Shells.
Analysis of Some Low-Order Finite Element Schemes for Mindlin-Reissner and Kirchhoff Plates.
Analytical and numerical study of some variants of Koiter's linear model of thin shells.
Koiter’s linear model for thin shells is obtained from the classic equations of the three-dimensional linear elasticity with the Kirchhoff-Love hypothesis; the variety of formulations of this model is based on the precision of the analysis carried out. In this work we detail these simplifications, and analyse the origin and the error of some variations of the model. We also approximate some of these versions by a nonconforming finite element method and compare the numerical results over some classical...
Analytical solution for different profiles of fin with temperature-dependent thermal conductivity.
Aposteriorní odhady chyby v metodě konečných prvků
Approssimazione di flussi a superficie libera mediante modelli di Boussinesq
Approximation and numerical solution of contact problems with friction
The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function on a certain convex set . The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa’s algorithm is used. Some examples are given in the conclusion.
Approximation numérique du cisaillement transverse dans les plaques minces en flexion.