Direct Computation of Stresses in Elasticity Problems

Description

A new approach has been recently proposed for the mathematical formulation of the quadratic minimization problems that arise in three-dimensional linearized elasticity. Since the stresses can be immediately expressed in terms of the strains through the constitutive equation, this approach leads in effect to a quadratic minimization problem whose sole unknowns are the stresses. Thus the purpose of this proposal is to numerically exploit this new formulation. A key objective of this proposal will consist of describing finite element spaces in which the Saint Venant compatibility conditions can be "approximated at best", as well as specifying how the terms involving the applied forces and the imposed boundary conditions can be conveniently taken into account into such finite element spaces. Another objective will be to establish the convergence of the "discrete stresses" obtained in this fashion toward the actual stresses, often regarded as the most relevant unknowns in computational mechanics.