Topological Optimization Of Engineering Structures Based On Homogenization Method With Triangular Voids Microstructure

The topology optimization problem for continuous structures is an attractive field in the structural optimization society. The homogenization method is one of the relatively active approachs for this problem. In this paper, the state of the art about topology optimization with homogenization method is introduced briefly.Different material microstructure models are described,the analytical solution of the volume function and relatively density function for the so called "rank laminate composites" microstructure and the microstructure consisting of an isotropic material with rectangular voids are presented. Using the homogenization theory and the periodicity assumption, the model for the topological optimization of engineering structural based on homogenization method with triangular voids microstructure is provided.The mathematical model for the topological optimization of engineering structures based on homogenization method with triangular voids microstructure is constructed. Derivation of the related optimality criteria is explained, and a modified resizing scheme is suggested, the describe functions for homogenization are solved. At the last, some illustrative examples are provided. Both the similarities and differences in macroscopical level and microscopical level are discussed between triangular voids structure and rectangle voids structure through the result of the examples.Finally, The future perspectives of topology optimization designs and some problems to be solved about homogenization method are outlined.