Research On Improved Parametric Level Set Topology Optimization Method And Applications

Topology optimization is an optimal design method to obtain one or more optimal performances of a structure subject to design constraints inside the given design domain. Its application range involves aerospace engineering, automobile industry, biological engineering, materials engineering, civil & hydraulic engineering and energy industry, etc. Topology optimization is able to improve the structural performances, reduce the structural weight and shorten the development cycle. Furthermore, it is also can be applied to innovative design problems of complex structures, which may not be solved by the traditional design methods. Structural topology optimization has gained certain improvement due to the rapid development of the computer technology, finite element method and mechanics theory. Comparing to the traditional topology optimization methods, the level set based topology optimization methods are able to achieve the topology and shape optimization simultaneously, and maintain the smooth structural boundary and clear geometry information of the optimal result. Thus, these methods have attracted a wide range of attentions and investigations. Nevertheless, the conventional level set methods have several disadvantages, which prevent their further development and application. This thesis proposes the countermeasures to overcome the numerical issues of the conventional level set methods, and then implements the proposed approaches into the structural topology optimization under multiple loading cases, structural frequency response topology optimization, extrusion-based structural topology optimization and integrated topology optimization of cellular materials and structures.Firstly, the topology optimization method based on the parametric level set is studied. To eliminate the numerical difficulties in the traditional level set methods, the parametric level set method using compactly supported radial basis function(CSRBF) and discrete wavelet transform(DWT) is proposed. Then the structural stiffness topology optimization model based on the parametric level set method is formulated. The design sensitivity based on the shape derivative is derived. The optimization algorithm based on the optimality criteria method is developed. The structural topology optimization design by using the parametric level set method is achieved. In the proposed method, the CSRBF is utilized to interpolate the level set function to effectively avoid the numerical issues caused by the direct solution of the complex Hamilton-Jacobi partial differential equation, and the DWT is adopted to compress the interpolation matrix aroused by the CSRBF to further increase the computational efficiency.Secondly, the topology optimization under multiple loading cases based on the parametric level set method is studied. Considering the research status of this problem, the multiobjective optimization modelling method by incorporating the parametric level set method with the normalized exponential weighted criterion(NEWC) is proposed, in order to eliminate the ill-conditioned loading issue and obtain the Pareto optimal solution on the non-convex Pareto frontier. With regard to the determination of the weights of subobjectives, a weight evaluation method based on the fuzzy multiple-attribute group decision-making(FMAGDM) is developed to reduce the influences of subjective factors. We first investigate the topology optimization problem under multiple loading cases considering the concept of extended optimality, which simultaneously optimize the compliance under each loading case and the structural volume fraction, so as to obtain the optimal structure with less weight.Thirdly, the topology optimization of structural frequency response based on the parametric level set method is studied. For the different types of structural frequency responses, the topology optimization methods of the global and local frequency response are proposed by using the parametric level set, which can ensure the smooth structural boundaries and effectively improve the structural dynamic performance. Considering the finite element analysis of structural frequency response under excitation frequency range, the multifrequency quasi-static Ritz vector(MQSRV) is introduced to reduce the finite element model. Therefore, the computational costs of repetitive calls for the finite element analysis are reduced.Fourthly, the topology optimization of extrudable structure based on the parametric level set method is studied. We investigate the topology optimization technique of extrudable structures mainly from two aspects, i.e. the structural boundary and cross section. With regard to the structural boundary, the extrusion-based structural topology optimization model by using the proposed parametric level set method is formulated, so as to guarantee the complete geometry information of the optimal topology. Considering the design requirement of uniform structural cross sections, the extrusion constraints are introduced, and the cross section projection approach is proposed to handle the extrusion constraints. In doing so, the manufacturability of optimal design can be guaranteed, while the efficiency of the optimization method is also increased.Fifthly, the integrated topology optimization of cellular materials and structures based on the parametric level set method is studied. Considering the computing efficiency and manufacturing cost of the recent integrated topology optimization design of the materials and structures, the two-stage method is proposed. At the macrostructural layout optimization design stage, the SIMP(solid isotropic microstructures with penalization) material density interpolation scheme is used to obtain the layer-wise density distribution within the design domain. At the material microstructure topology optimization design stage, the parametric level set method is utilized to describe the microstructural boundary, to obtain the material microstructural layouts with smooth boundaries as well as various macroscopic equivalent properties. The optimal materials and structures with multiple functional properties are achieved via assembling the optimal results of the two design stages.Sixthly, the proposed methods are applied to two practical engineering problems. Results indicate that the proposed method can greatly simplify the procedure of structural design, improve the structural performances and accomplish the light-weight design of engineering products. The proposed methods can efficiently support the structural optimization design of engineering products.Finally, the conclusions of research goals and main innovative points are given and the prospects for further research work are outlined.