Generalized Inverses in Elastic-Plastic Analysis of Structures∗

This paper deals with elastic-plastic analysis of skeletal structures that are subjected to proportionally increasing loading. It is assumed that no local unloading occurs (holonomic behavior) and that yield conditions are piecewise linearized. A quadratic programming problem, which arises from the application of the minimum complementary energy principle for such structures, is shown to have an explicit form of solution. The matrix expression of this solution involves certain modifications of the Bott-Duffin generalized inverse. This inverse can be effectively calculated for a given structure and allows one to obtain a unique stress distribution under agiven load. Moreover, if the load is prescribed up to an unknown scalar factor, the ultimate value of this multiplier (collapse load) and the elastoplastic stress state at collapse can be found by the same method