Yield design theory: an efficient static method formulation

Abstract

Numerical formulations for determining extreme loads within the framework of yield design theory require non-linear optimization problems with constraints to be resolved. The difficulty which is presented by these optimization problems still greatly limits practical applications, in particular those concerning three-dimensional mechanical systems. For a class of materials whose strength domain is defined by positively homogeneous functions and contains in its interior the zero stress tensor, a new formulation of the static method is established here. This particular formulation leads to a minimax discrete problem without constraints which uses a reduced number of variables. Numerical resolution of this minimax problem is based on a regularization of the objective function. Applications concerning the calculus of the macroscopic tensile strength of a periodically heterogeneous medium and the study of the stability of a vertical cut enables the performances of the program developed to be analyzed.