Artificial boundary conditions to compute correctors in linear elasticity

Artificial boundary conditions to compute correctors in linear elasticity

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...

Exact Artificial Boundary Conditions for Continuum and Discrete Elasticity

For the continuum and discrete elastic equations, we derive exact artificial boundary conditions (ABCs), often referred to as transparent boundary conditions, that can be applied at a planar interface below which there are no forces. Solution of the elasticity equations can then be performed using this interface as an artificial boundary, often with greatly reduced computational effort, but wit...

Integrability of Displacement and Stresses in Linear and Nonlinear Elasticity with Mixed Boundary Conditions

Equations of linear and nonlinear infinitesimal elasticity with mixed boundary conditions are considered. The bounded domain is assumed to have a Lipschitz boundary and to satisfy additional regularity assumptions. W 1,p regularity for the displacements and Lp regularity for the stresses is proved for some p > 2.

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...