On the numerical solution of a class of unilateral contact structural optimization problems

This paper deals with a special class of structural optimization problems i n nonsmooth mechanics. More precisely, it is required to minimize the weigh t of a structure subject to frictionless unilateral contact conditions and constraints on the magnitudes of contact forces, displacements, stresses an d cross-sectional areas. This problem, as is well-known, can be formulated as a special and challenging optimization problem known as a Mathematical P rogram with Equilibrium Constraints (MPEC), a key feature of which is the p resence of complementarity conditions, involving the orthogonality of two s ign-constrained vectors. In spite of its inherent nonsmoothness, we attempt to solve the problem using standard nonlinear programming techniques. In p articular, we investigate numerically the application of two simple algorit hms, both based on the use of the general-purpose nonlinear programming cod e CONOPT accessed via the powerful GAMS modelling language, for solving the suitably reformulated problem. Application is illustrated by means of thre e numerical examples.