Topology Optimization of Sheets in Contact by a Subgradient Method

We consider the solution of nite element discretized optimum sheet problems by an iterative algorithm. The problem is that of maximizing the stiiness 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 nondiierentiable, convex minimization problem in the displacement variables. The convergence of this method is proven, and its low computational complexity is 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 eeciency of the algorithm and investigate the properties of the optimal designs, the algorithm is numerically tested on some medium and large scale problems.