Research on Topology Optimization Method for Continuum Structure under Geometric Constraints

A new topology optimization model with holes' geometric constraints for continuum structure is presented. It is solved by an evolutionary optimization method based on interval relaxation, in which the problem is divided into two subproblems of topology optimization process and size/shape optimization process. The optimal topology of structure can be found gradually by introducing interval relaxation factor to adjust holes' size constraints, delete noneffective holes and by generating new holes based on the sensitivity analysis of objective function. Interior penalty-function method is employed as an optimization technique for the size/shape optimization of the structure corresponding to the topology. When the holes' size bounds are the actual values, the optimal solution is the smallest objective function structure in the various topologies. Thus realizes the holes' geometric size and location design, topology design and layout design together. The optimization results of example shows the method proposed is of good effectiveness and engineering applicability.