Optimization of continuous elastic perfectly plastic beams

The optimal design of elastic plastic beams subjected to loads quasi-statically variable within a given domain is studied. A minimum volume formulation and a maximum load multiplier formulation are developed, both expressed on the grounds of a statical as well as of a kinematical approach. The search problems are formulated according to three different limiting criteria acting simultaneously. For each criterion a corresponding selected safety factor is imposed. The Euler–Lagrange equations related to the above described problems are deduced. A special iterative technique devoted to the solution of the above referenced problems is proposed. Some numerical examples conclude the paper.