Triangulation Method for Approximate Solving of Variational Problems in Nonlinear Elasticity

Abstract

A variational problem for the minimum of the stored energy functional is considered in the framework of the nonlinear theory of elasticity, taking into account admissible deformations. An algorithm for solving this problem is proposed, based on the use of a polygonal partition of the computational domain by the Delaunay triangulation method. Conditions for the convergence of the method to a local minimum in the class of piecewise affine mappings are found.

Keywords

• stored energy functional
• variational problem
• gradient descent method
• delaunay triangulation
• finite element method