Topology Optimization of Typical Beam Structures Based on Level Set Method

Abstract

This paper takes the minimum flexibility of the structure as the objective function and the volume ratio of the solid material as the constraint condition to realize the topology optimization of the level set method. The radial basis function (RBF) can be used to interpolate discrete points into smooth curves, and the level set function can be used to implicitly describe the structure boundary. By designing the initial structure of the hole, it is obtained that the optimization result will be better if the hole is as wide as possible in the whole area. Through many experiments, it is proved that the restraint condition is that the remaining material volume ratio of 50% is more reasonable than other ratios. The effectiveness of the proposed method is verified by two classical examples of cantilever beam and simply supported beam. Comparing with the variable density method, the checkerboard format of gray level unit is eliminated, the smooth boundary is obtained, and the efficiency of hole nucleation is improved.