This paper develops least-squares methods for the solution of linear elastic problems in both two and three dimensions. Our main approach is defined by simply applying the L2 norm least-squares principle to a stress-displacement system: the constitutive and the equilibrium equations. It is shown that the homogeneous least-squares functional is elliptic and continuous in the H(div; Ω)d × H1(Ω)d ...

Energy estimates show that linearized thermo-elasticity deenes a contraction semi-group on a Hilbert space. We show that under a geometric condition this contraction is not strict, or, more precisely, the norm of the semi group is 1 for all t 0. Convex domains always satisfy the geometric condition. 2. introduction Let R n be a bounded domain with smooth boundary ?. We consider the problem @ 2 ...

c = c = c . (2) 1 We use the notation of Schouten [9]. Symmetrization over two indices is denoted by parentheses, A(ij) := (Aij + Aji)/2!, antisymmetrization by brackets, B[ij] := (Bij − Bji)/2!. The analogous is valid for more indices, as, e.g., in (13): c i[jk]l = (c − c)/2!. If one or more indices are exempt from (anti)symmetrization, they are enclosed by vertical bars, as, e.g., in (12), c ...

We present some new formulae for the solution of boundary value problems for a two-dimensional isotropic elastic body. In particular, using the so-called Dbar formalism and the method introduced by Fokas (2008) [4], we obtain integral representations of the Fourier type for the displacements appearing in boundary value problems formulated in an arbitrary convex polygon with n sides. © 2011 Else...

Two-dimensional linear elasticity problems are approximately solved by a mixed finite-element method based on Raviart-Thomas-Nedelec spaces; maximum-norm error estimates of optimal rate and almost optimal regularity are derived for the displacement field, and of optimal regularity and almost optimal rate for the stress tensor. The superconvergence of the approximate displacement field to the L2...

Conditions for Stable Approximation Schemes Basic idea: Mimic structure of continuous problem. To establish stability of continuous problem, only used last two spaces in top sequence and last three spaces in bottom sequence. Λn−1(K) dn−1 −−−→ Λn(K)→ 0 ↗ Sn−2 ↗ Sn−1 Λn−2(V) dn−2 −−−→ Λn−1(V) dn−1 −−−→ Λn(V)→ 0. Thus, look for five finite dimensional spaces connected by a similar structure, i.e.,...

In this paper, surface effects including surface elasticity, surface stress and surface density, on the free vibration analysis of Euler-Bernoulli and Timoshenko nanobeams are considered using nonlocal elasticity theory. To this end, the balance conditions between nanobeam bulk and its surfaces are considered to be satisfied assuming a linear variation for the component of the normal stress thr...

The aim of this paper is to extend, to the linear elasticity system, the asymptotic analysis by compensated compactness previously developed by the authors for the linear diffusion equation. For simplicity, we restrict ourselves to stratified media. In the case of sole homogenization we recover the classical result of W.H. Mc Connel, deriving explicitly the effective elasticity tensor for strat...