Global meshless solutions for elasticity problems with direct enforcement of boundary constraints

In this work we present a meshless method based on the minimum total energy principle for solving elasticity problems. The problem is reformulated as a convex quadratic programming one with equality constraints for which very efficient numerical solvers exist. We will show that this formulation is a generalization of the classical Element-Free Galerkin (EFG) method and, in combination with an enriching function technique, it exhibits very good performances without the need of an extreme discretization refinement.