Universal displacements in linear elasticity

Integral representations of displacements in linear elasticity

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...

On Rigid and Infinitesimal Rigid Displacements in Three-Dimensional Elasticity

Let Ω be an open connected subset of R and letΘ be an immersion from Ω into R. It is first established that the set formed by all rigid displacements, i.e., that preserve the metric, of the open set Θ(Ω) is a submanifold of dimension 6 and of class C∞ of the space H(Ω). It is then shown that the vector space formed by all the infinitesimal rigid displacements of the same set Θ(Ω) is nothing but...

A Discrete Differential Sequence for Elasticity Based upon Continuous Displacements

The present paper introduces a mixed stress-displacement method for linear elasticity, as an extension of the work performed by Christiansen [15] for computational relativity. Moreover, we establish self-adjointness in a special sense and perform numerical simulations to assess the relevance of the method, including comparison with the recent TDNNS [30, 34] mixed formulation. Extensions to high...

En224: 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 ...