Feasibility of a numerical method for computing the ultimate loads of three-dimensional structures (Q1905518)

We introduced earlier a vector potential technique to generate virtual velocity fields which satisfy zero volume change constraints automatically. The problem then amounts to the minimization without constraints of a function depending on a finite number of variables. Whereas this method was successfully implemented in the case of plane strain conditions, its extension and practical implementation for the treatment of truly three-dimensional problems was only outlined. The purpose of the present paper is focused on its feasibility in the latter case. As an illustrative example, the classical problem of punch indentation is examined. The numerical results are compared with an analytical approach giving an upper bound estimate of the load required to produce indentation.