Skip to content
BY-NC-ND 4.0 license Open Access Published by De Gruyter January 1, 2011

Energy Principles and Finite Element Methods for Pure Traction Linear Elasticity

  • Pavel Bochev EMAIL logo and Richard Lehoucq


A conforming finite element discretization of the pure traction elasticity boundary value problem results in a singular linear system of equations. The singularity of the linear system is removed through various approaches. In this report, we consider an alternative approach in which discrete finite element formulations are derived directly from the principle of minimum potential energy. This point of view turns out to be particularly well suited to handle the rigid body modes, which are the source of the singularity in the finite element linear system. Our approach allows us to formulate a regularized potential energy principle and show that the associated weak problem is coercive in H1(Ω). This guarantees nonsingular problems, enables simplified solution algorithms and leads to more efficient and robust preconditioners for the iterative solution linear equations.

Received: 2010-11-17
Revised: 2011-03-28
Accepted: 2011-06-20
Published Online: 2011
Published in Print: 2011

© Institute of Mathematics, NAS of Belarus

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Downloaded on 31.3.2023 from
Scroll to top button