New type of optimal topologies by iterative method

Optimal design with thousands of variables is a great challenge in engineering calculations. In this paper beside the short history of optimality criteria methods, a solution technique is introduced for the topology optimization of elastic disks under single parametric static loading. Different boundary conditions and thousands of design variables are applied. Due to a simple mesh construction technique, the checker-board pattern is avoided. The Michell-type problem is investigated minimizing the weight of the structure subjected to a compliance condition. The numerical procedure is based on an iterative formula that is formed by the use of the. first-order optimality condition of the Lagrangian function. The application is illustrated by numerical examples. The effect of the different loading conditions is studied for the Michell-type topologies as well.