Optimal Truss Design with Elastic and Plastic Collapse Constraints

Optimal design of trusses is presented using several approaches, in which weight is minimized for a prescribed load. The model proposed comprises the full range of strictly elastic, elastic/plastic and strictly plastic designs. As a result, dimensionally optimal structures are found under stress and displacement constraints, together with constraints imposed on safety factor during plastic collapse. In this problem, collapse loading is a nonsmooth function of the design variables which may cause some undesirable behavior. Nonsmoothness is thus treated using optimization techniques, in which safety factor is judiciously smoothned out with respect to the plastic collapse constraint. Under these considerations, it is possible to obtain lighter structures while maintaining their reliability. Numerical examples illustrate the usefulness of these new formulations.