TOPOLOGY OPTIMIZATION OF SHEETS IN CONTACT BY A SUBGRADIENT METHOD

We consider the solution of Þnite element discretized optimum sheet problems by an iterative algorithm. The problem is that of maximizing the sti¤ness of a sheet subject to constraints on the admissible designs and unilateral contact conditions on the displacements. The model allows for zero design volumes, and thus constitutes a true topology optimization problem. We propose and evaluate a subgradient optimization algorithm for a reformulation into a nondi ¤erentiable, convex minimization problem in the displacement variables. The convergence of the method and its low computational complexity are established. An optimal design is derived through a simple averaging scheme which combines the solutions to the linear design problems solved within the subgradient method. To illustrate the e¦ciency of the algorithm and investigate the properties of the optimal designs, the algorithm is numerically tested on some medium- and large-scale problems