Artificial conditions for the linear elasticity equations

Artificial conditions for the linear elasticity equations

In this paper, we consider the equations of linear elasticity in an exterior domain. We exhibit artificial boundary conditions on a circle, which lead to a non-coercive second order boundary value problem. In the particular case of an axisymmetric geometry, explicit computations can be performed in Fourier series proving the wellposedness except for a countable set of parameters. A perturbation...

Artificial boundary conditions to compute correctors in linear elasticity

Gradient schemes for linear and non-linear elasticity equations

The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numeri...

Nonconforming Finite Element Methods for the Equations of Linear Elasticity

In the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions, the main difficulty in the analysis is to prove that an appropriate discrete version of Korn's second inequality is valid. Such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears. Op...

On the Compatibility Equations of Nonlinear and Linear Elasticity in the Presence of Boundary Conditions∗

We use Hodge-type orthogonal decompositions for studying the compatibility equations of the displacement gradient and the linear strain with prescribed boundary displacements. We show that the displacement gradient is compatible if and only if for any equilibrated virtual first-Piola Kirchhoff stress tensor field, the virtual work done by the displacement gradient is equal to the virtual work d...