Structural Topology Optimization Based On Truss-like Model With Different Material Properties In Tension And Compression

Structural optimization, as an important means to design structures with higher performance and lower cost, has drawn researchers’ attention. With the development of computer technology and optimization theory, there are more and more achievements in topology optimization. So far, structural optimization method is widely used in many areas, such as aerospace, automobile manufacturing, and other machinery. However it was less applied in building structures relatively. The materials used in buildings always have different material properties in tension and compression. For now most of methods deal with structural topology optimization based on isotropic material model.Structural topology optimization based on truss-like model with different material properties in tension and compression, was studied in this paper. By modifying the material models, the concept of different material properties in tension and compression can be introduced to the structural topology optimization method. It is illustrated with a short cantilever structure optimization example that, full stress criterion optimization method cannot be used to resolve the optimization problem with different material properties in tension and compression. In order to test the accuracy of the optimization algorithm, the compliance of two-bar structure with different elastic modulus in tension and compression under the load in arbitrary direction is minimized by an analytical method. And the volume of two-bar structure with different allowable stress in tension and compression under the load in arbitrary direction is minimized by an analytical method too. These results can be used as benchmarks.The method of moving asymptotes is used to minimize the compliance of truss-like structure with different elastic modulus in tension and compression. It failed because the design variable of densities and the design variable of directions were quite different. So a new optimization algorithm processes was presented in this paper by modifying old one. And the new method was tested by the standard numerical examples from the third chapter. Some simple examples for practical application of engineering are showed here.In the fifth chapter, stress singularity problem was studied. The results of fully stressed criterion optimization method and MMA are compared. With the relaxation of the stress constraints and MMA together the stress singularity problem is dealt with. The magnitude of ε and the form of constraint expression influences the process of optimization iteration was studied, which provides ideas to solve stress-constrained minimum-weight topology optimization problems.