Optimal Plastic Synthesis of Structures with Unilateral Supports Involving Frictional Contact

We consider the optimal synthesis, namely minimum weight design, of rigid perfectly-plastic structures for which some supports involve unilateral frictional contact. This problem is of interest as it is not only encountered in practice but it also involves, in the general friction case, a nonassociative complementarity condition that makes it theoretically and numerically challenging. For simplicity of exposition, we focus on the class of bar structures for which yielding is governed by either pure bending or by combined axial and flexural forces. In view of possible multiplicity of solutions due to nonassociativity, a direct optimization formulation may lead to an unsafe solution. We therefore propose an efficient and robust iterative scheme that can provide a safe and optimal design. Underpinning the algorithm is a recently developed numerical procedure for solving the extended limit analysis state problem. Application is illustrated through three numerical examples.