Calculation of extreme loadings by solution of a minimax problem without constraints (Q1371260)

The authors consider plasticity and strength limit conditions satisfied by constraint tensor defined by means of homogeneous positive functions (as in the case of von Mises and Drucker-Prager criteria). A new optimization procedure is developed which leads to discrete minimax problems without constraints. The resulting regularization algorithm is very efficient and can be generalized to the case of fracture calculus with strength domains which are not convex but only star-shaped. Two examples are worked out: a rectangular plate with six quadratic holes, and a layered rectangular plate with given normal velocity on a side. The admissible strength is obtained for a number of conditions which does not exceed 38002 (from which 8192 are nonlinear).