ON LOCKING-FREE FINITE ELEMENT SCHEMES FOR THREE-DIMENSIONAL ELASTICITY

In the present paper,the authors discuss the locking phenomenon of the finite elementmethod for three-dimensional elasticity as the Laméconstant λ→∞.Three kinds of finiteelements are proposed and analyzed to approximate the three-dimensional elasticity withpure displacement boundary condition.Optimal order error estimates which are uniformwith respect to λ∈(0,+∞)are obtained for three schemes.Furthermore,numerical resultsare presented to show that,our schemes are locking-free and and the trilinear conformingfinite element scheme is locking.     

The Elastic Continuum Limit of the Tight Binding Model

The authors consider the simplest quantum mechanics model of solids,the tight binding model,and prove that in the continuum limit,the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule.The technique in this paper is based mainly on spectral perturbation theory for large matrices.