A Topological Optimization Method of Similar Periodic Structures Based on Variable Displacement Limits

A distinctive topology configuration can be obtained when the design domain has a similar size in all directions for a plane or three-dimensional problem. However, it is difficult to solve the topology optimization problem for a long-and-thin structure with variable cross-section using conventional algorithm. In order to solve this problem, a new method for topology optimization of similar periodic structures is proposed, based on the ideas of the variable displacement constraint limits. To satisfy the similar periodic constraint, the design domain is divided into a certain number of similar sub-regions which have the same number of elements. Relations of the relevant elements of different sub-regions are established. A mathematical programming formula and its procedure are proposed, being based on the idea of the independent, continuous and mapping method. And a set of displacement approximate formulation is derived and a new topology optimization method is developed and implemented. Several simulation examples show that the proposed method is of validity and effectiveness.