Static Topology Optimization Design Of Continuum Structures Under Stress And Displacement Constraints

In recent decades, with the developed mathematical theory and enhanced performance of computational tools, optimization design developed rapidly, which combines mathematical optimization theory and engineering design, people can select the best one from the numerous in solving design problems, and improve design efficiency and design quality.Structural optimization design can not be separated from engineering practice, so this paper studied on static topology optimization design of continuum structures under stress and displacement constraints mainly used the mathematical optimization method, theoretical modeling and numerical simulation methods.Used MATLAB to program procedures about rectangular element finite element plane stress, compared with the results of commercial software ANSYS.Based on the ICM (Independent Continuous Topological Variables and Mapping Transformation) method, a model with weight objective and displacement constraints was established, used MATLAB software platform to achieve ICM method. The effectiveness of the method was analyzed.To address the low continuous variable field generated by unit variable, replaced unit variable with node variable, a model with weight objective and nodal displacement constraints was established for the topology optimization design of continuum structures. The model was simplified by duality theory. And the results with node-based ICM method were compared.Considered stress constrained optimization problem by establish structural weight as objective function, the node stress as constraints, node topology value as design variable. Solved the node topology variables with fully stress. To improve a large number of stress concentration generated by the fully stressed design method, used add or delete artificial elements method to average stress, obtained satisfavtory results.For the optimization problem with displacement and stress common constraint, by criterion, changed the stress constaints into a dynamic threshold for design variables. Solved the model by quadratic programming and analyzed the results in the end.