Research And Analysis Of Topology Optimization Algorithm For Mechanical-electrical Coupling Problem

Piezoelectric materials as structural and functional materials have mechanical and electrical coupling properties,so it is widely used in various fields of engineering.In daily life,changing the position,size,shape and other parameters of piezoelectric components in piezoelectric intelligent structure can effectively improve the mechanical properties of the system,so the research of topology optimization design of piezoelectric intelligent structure has become more and more important.The first part of this paper focuses on the topology optimization algorithm for the power coupling problem of homogeneous materials.Based on the power coupling constitutive equation of piezoelectric materials,a topology optimization algorithm for the power coupling problem of homogeneous materials is constructed.Firstly,the structural algorithm and finite element modeling are used to simulate the topology of a two-dimensional cantilever beam design problem by using solid isotropic material penalty method.Secondly,a program is used to calculate and optimize the optimal structure of the cantilever design field under the influence of power coupling.Finally,numerical results show that the proposed algorithm is effective.In the second part of this paper,the homogeneity problem of electro-mechanical coupling in the topology optimization of composite materials is proved by using the two-scale asymptotic method.By solving piezoelectric composites an algorithm for topology optimization of piezoelectric composites is obtained and applied to two dimensional holes the numerical results show that the results of equivalent homogeneous materials are similar to those of fine mesh composites.Therefore,the power coupling topology optimization algorithm based on homogenization theory is effective.