A lumped stress method for plane elastic problems and the discrete-continuum approximation

This paper proposes a rational method to approximate a plane elastic body through a latticed structure composed of truss elements. The method is based on the introduction of a relaxed stress energy that allows an extension of the original problem to a larger space of admissible stress fields, including stresses concentrated along lines. Use is made of polyhedral approximations of the Airy stress function. The truss analogy is employed to obtain a displacement formulation. The paper includes several numerical applications of the method to sample problems, a numerical convergence study and comparisons with exact solutions and standard finite element approximations