Ultimate state of plane frame structures with piecewise linear yield conditions and multi-linear behavior: A reduced complementarity approach

• A new approach for elastoplastic analysis with mathematical programming is presented.
• The yield condition is formed only for one hyperplane for each cross section.
• The formulation becomes independent from the linearization of the yield surface.
• Multi-linear hardening is incorporated without affecting the size of the problem.
• Numerical results verify the effectiveness of the approach.

Elastoplastic analysis of structures with mathematical programming methods aims at finding the load factor of a given load pattern subject to equilibrium and compatibility requirements, satisfying yield and complementarity constraints. A new approach is introduced that identifies the specific yield hyperplanes associated with all critical sections avoiding all irrelevant alternatives. This results into substantial reduction of the size of the yield and complementarity conditions. In addition, it has a beneficial effect in addressing multi-linear hardening and/or softening holonomic behavior by controlling the size of the problem. Numerical examples are presented that verify the efficiency of the proposed approach.