Research On Topology Optimization Method Based On Multi-field Coupling Piezoelectric Ceramic Structure

Piezoceramic materials has high sensitivity,and high piezoelectric performance,and are widely used in energy harvesting,smart power generation and other fields,and is considered to be one of the most promising smart materials.In the application of high-tech fields,the temperature usually changes obviously,such as when satellites and spacecraft are orbiting 300-500 kilometers from the ground,the ambient temperature changes from-150~℃-300~℃,and Piezoceramic materials’structure and piezoelectric performance will be significantly affected.so it is of theoretical and engineering significance to study this thermo-mechanical-electric coupling effect.With the increasingly fierce competition in technology,the environmental impact and shortage of resources,we urgently need to develop more lightweight,low-cost and low thermal sensitivity piezoelectric ceramic structures.Topology optimization is considered to be one of the most effective methods for structural optimization layout,which can not only maximize the performance of materials but also save materials.At present,the simulation analysis of piezoelectric thermos-elasticity is mostly solved by methods such as integral transformation and Laplace transform,which is not only complicated in calculation and low in calculation accuracy;the topology optimization design for piezoelectric ceramics mostly focuses on its electromechanical coupling effect and the single piezoelectric ceramic,the energy conversion efficiency of a single piezoelectric ceramic is relatively low.In view of the above problems,this paper establish a piezoelectric thermoelastic coupling model and use direct finite element method to simulate the thermo-mechanical-electrical coupling effect of piezoelectric ceramics,and adopt the variable density method to optimize the thermal-mechanical-electrical coupling topology design of piezoelectric ceramics;in order to improve the piezoelectric performance of piezoelectric structure,the piezoelectric ceramic-metal composite is optimized for multi-field coupling topology to make it more suitable for multi-field coupling environment.The main work of this article is as follows:Firstly,the finite element modeling and analysis of piezoelectric thermos-elasticity are carried out.The generalized thermos-elasticity theory is used to study the piezoelectric thermos-elasticity problem.The free energy function is introduced to obtain the governing equation of generalized piezoelectric thermos-elasticity.Based on the governing equation and the L-S thermos-elastic theory,the piezoelectric displacement model is established using the virtual displacement principle;The direct finite element method is used to simulate the temperature,displacement,and potential distribution trends of two-dimensional piezoelectric ceramic plates.Then,the multi-field coupling topology optimization design of a single piezoelectric ceramic is carried out,basing on the piezoelectric thermos-elastic model,and using the maximum piezoelectric conversion efficiency as the objective function to determine the piezoelectric thermos-elastic topology optimization model;Adopting the adjoint method to derive the objective function,and using the method of moving asymptotes to solve;the topological optimization design of the two-dimensional piezoelectric ceramic cantilever structure has significantly improved the piezoelectric conversion efficiency.Compared with the optimized structure with the same mechanical load and different temperature increments,and the mechanism of the thermal effect on the piezoelectric ceramic structure is obtained.Finally,the multi-field coupling topology optimization method for piezoelectric ceramic-metal multiphase materials is studied.Based on the SIMP model multiphase material interpolation method,the parameters of piezoelectric ceramic-metal multiphase materials are interpolated to determine the stiffness matrix of the multiphase materials.Then,establish a multi-field coupling topology optimization model of three-phase materials of piezoelectric ceramics,metals and empty materials,and the topology optimization design of the two-dimensional piezoelectric ceramic-metal cantilever structure.