Optimum design of plastic structures under displacement constraints

This paper deals with the optimum design under given loads, of discrete (truss-like) linearly hardening or non-hardening plastic structures, subject to limitations on displacements and deformations and to linear technological constraints. Basic assumptions are: (i) the "cost" function is linear in the design variables; (ii) no local unstressing occurs under the given proportional loading, so that holonomic plastic laws can be adopted. Both elastic-plastic and rigid-hardening models are considered. A typical mathematical feature of the optimization problem is a (nonlinear, nonconvex) complementarity constraint. For situations where the local resistances, assumed to be design variables, do not affect the local stiffness, a branch-and-bound method is proposed and an alternative quadratic programming approach is envisaged. For situations where local strength and stiffness are coupled, a method is developed consisting basically of iterative applications of the procedure devised for uncoupled cases. The computational efficiency of the solution methods proposed is examined by means of numerical tests.