MMC-based Topology Optimization Considering The Natural Frequencies Of Continuum Structures

Topology optimization is a hot topic in the field of computational mechanics and is becoming an indispensable tool in practical engineering.After more than 30 years of development,the technology has been applied and played an active role in high-end manufacturing industries such as aerospace,vehicle and rail transit.Topology optimization considering the dynamic performance of structures is one of the most challenging and difficult problems in this field.In the traditional implicit framework,the problems such as huge computation,unstable convergence process and localized eigenmodes are encountered when solving the problem,so its application in practical engineering still faces many challenges.In recent years,explicit topological optimization methods have been paid more and more attention in academia.This kind of methods can obtain topological structures with explicit geometric boundaries,avoid the localized eigenmodes at weak elements in traditional density methods,and have fewer design variables and less computation.Based on the significant advantages of this method,this paper adopts the explicit Moving Morphable Components(MMC)method to carry out topological optimization design for the natural frequency of continuous structure.Specific research contents include:Firstly,consider explicit topological optimization methods have not yet been used in the field of structural dynamics,the explicit geometric description of the physical quantities related to the structural topology and dynamic performance of the structure is realized based on the MMC topology optimization framework,a primitive moving morphable component parametric representation method is defined,established the optimization scheme of natural frequency correlation topology optimization problem.Secondly,based on the MMC method,the topological optimization design of the continuum structure with fundamental frequency maximization/minimization and given fundamental frequency constraints are realized,and the convergence stability and advantages of the proposed method are emphatically investigated.Based on an explicit geometric boundary expression,the optimal structure can directly import into commercial CAD/CAE software to verify the optimal result by finite element analysis.Thirdly,based on the MMC method,the maximization of high-order natural frequency of continuum structure and the maximization of the difference between adjacent natural frequencies are realized.In order to solve the common problems of multiple frequencies and modal exchange in the topological optimization of high order natural frequency optimization,the corresponding sensitivity analysis method and modal tracking technique were used respectively in the explicit frame.The problem of convergent curve oscillation in the process of optimization is discussed in detail.This study provides a new idea for topology optimization of dynamic performance of continuum structures.Because the topological optimization method captures the essence of the "topology",the optimization object is the real structure rather than the mathematical model interpolated by pixel or node.It has great potential in reducing the computation cost of topological optimization and structural analysis,seamless connection with CAD/CAE system,and application in large-scale engineering structures.Numerical examples show that the MMC method has the characteristics of high efficiency and stability in dealing with the structural natural frequency optimization,which fundamentally solves the above difficulties in the topological optimization of structural dynamic performance.