Successive linear approximation for finite elasticity

Finite Element Methods for Linear Elasticity

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.,...

Plane wave approximation in linear elasticity

Hybrid Stress Finite Volume Method for Linear Elasticity Problems

Abstract. A hybrid stress finite volume method is proposed for linear elasticity equations. In this new method, a finite volume formulation is used for the equilibrium equation, and a hybrid stress quadrilateral finite element discretization, with continuous piecewise isoparametric bilinear displacement interpolation and two types of stress approximation modes, is used for the constitutive equa...

A Mixed Nonconforming Finite Element for Linear Elasticity

This article considers a mixed finite element method for linear elasticity. It is based on a modified mixed formulation that enforces the continuity of the stress weakly by adding a jump term of the approximated stress on interior edges. The symmetric stress are approximated by nonconforming linear elements and the displacement by piecewise constants. We establish (h) error bound in the (broken...

Symmetric Nonconforming Mixed Finite Elements for Linear Elasticity

We present a family of mixed methods for linear elasticity, that yield exactly symmetric, but only weakly conforming, stress approximations. The method is presented in both two and three dimensions (on triangular and tetrahedral meshes). The method is efficiently implementable by hybridization. The degrees of freedom of the Lagrange multipliers, which approximate the displacements at the faces,...