A Unified Topology And Shape Optimization Method Under Geometric Constraints

This work is supported by the Natural Science Foundation of China ‘A study oftopology and shape optimization under geometric constraints for continuum structure’(Grants: No.50975107). Existing structural optimization methods are within certain limitsto solve the problem of the integration of topology optimization, shape optimization andsizing optimization. This paper presents a level set-based method to characterize thegeometric features, and a sizing optimization for geometric constraints can be achieved aswell as simultaneously topological shape optimization. Furthermore, the method issuccessfully extended to the compliant mechanism design, and structural dynamicsoptimal design.Firstly, the fundamental theory of standard level set method and parameterized level setmethod are discussed, as well as their advantages and disadvantages. Based on thisformula, in order to address the problem of sizing design or position design for regularholes, a parameterization level set-based sizing optimization method is proposed byconsidering the regular holes as the geometric constraints. In this method, the advantage ofthe implicit representation and parameterized expression is fully taken into account, andprovides the prerequisite for the construction of unified optimization model.Secondly, a unified optimization model is built by combining the topological shapeoptimization model with the sizing optimization model, and further inferred the sensitivityanalysis results for optimization criterion method. At the same time, some numerical skillsare studied to solve the numerical problems in the present method, such as the interferedissue and tolerance zone for regular holes.Thirdly, In order to address the problem of zigzag boundary in topology optimizationusing the Conventional Finite Element Method (CFEM), an extended Finite ElementMethod (XFEM) is introduced into the presented unified optimization model. The XFEMscheme has a high accuracy in boundary elements, which greatly increased the smoothnessof the boundary and saved the computing time, the convergence property and theconvergence efficiency of the algorithm are also improved.Finally, the unified optimization method is applied to design a new LED arm, the influence of topology, shape and size are considered simultaneously, the optimal resultsgreatly increased the first eigenfrequency of the arm. The actual project demonstrates theadvantages and generality of the presented method in dynamics optimal design.