Topology Optimization of Sheets in Contact by a Subgradient Method

We consider the solution of finite element discretized optimum sheet problems by an iterative algorithm. The problem is that of maximizing the stiffness 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 non-differentiable, 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 efficiency of the algorithm and investigate the properties of the optimal designs, thealgorithm is numerically tested on some medium- and large-scale problems. © 1997 by John Wiley & Sons, Ltd.