Problems in mechanics such as limit analysis of beams and plates are studied. The above limit analysis problems are embedded in a wider class of nonsmooth functionals (involving a linear weighted least-squares problem), which contains also some location problems (e.g. the Fermat- Weber problem). An algorithm is proved for minimizing the functionals in the above class, which is based on a combination of smoothing and successive approximation (CSSA). This CSSA algorithm is a modification of that by W. H. Yang [Comput. Methods Appl. Mech. Eng. 33, 575-582 (1982; Zbl 0478.73022)].
A convergence analysis of the CSSA algorithm is presented including an excellent performance of the algorithm in the first step, regardless of the starting point. A dual problem to the smoothed primal is derived. It is shown how to obtain a stopping criterion for the algorithm and an estimation of the solution error. Computational results are presented for two limit analyses: a small-scale three bar truss and a large-scale simply supported square plate.