On Reissner's variational theorem for boundary values in linear elasticity

About Clapeyron’s Theorem in Linear Elasticity

We examine some elementary interpretations of the classical theorem of CLAPEYRON in linear elasticity theory. As we show, a straightforward application of this theorem in the purely mechanical setting leads to an apparent paradox which can be resolved by referring either to dynamics or to thermodynamics. These richer theories play an essential part in understanding the physical significance of ...

A Galerkin Boundary Node Method for Two-Dimensional Linear Elasticity

In this paper, a Galerkin boundary node method (GBNM) is developed for boundary-only analysis of 2D problems in linear elasticity. The GBNM combines the variational form of a boundary integral formulation for the elastic equations with the moving least-squares approximations for generating the trial and test functions. Unlike the boundary node method, the main idea here is to use the Galerkin s...

Coupled variational formulations of linear elasticity and the DPG methodology

This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually well-posed family of broken variational formulations of the original PDE. It can be exploited to solve challenging problems in a variety of physical scenarios where ...

Artificial boundary conditions to compute correctors in linear elasticity

Linear boundary values of weakly quasiregular mappings

We use a new construction in the spirit of Gromov’s convex integration to prove a rather surprising result that every affine map is the boundary value of a weakly quasiregular map in any Sobolev space with index p < n/2. Our method is based on constructing special Cauchy sequences by convex integration for certain vectorial Hamilton–Jacobi equations.  2000 Académie des sciences/Éditions scient...