Topology Optimization Design Of Piezoelectric Composite Energy Harvesting Devices Based On Parametric Level Set Method

The topology optimization is introduced to find the optimal material distribution under the given constraints,load and boundaries in the conceptual design stage,which can effectively overcome the blindness of traditional design and realize the intelligent design.The application of topology optimization design to piezoelectric energy harvesting structure can play the greatest potential of piezoelectric materials,design the best performance of the structure.In order to solve the problem that the boundary is unclear,the checkerboard phenomenon based on SIMP method,the low efficiency based on standard level set method,the low performance of single material and poor manufacturability,thus a parameterized level set method for the optimum design of piezoelectric energy harvesting structure is proposed,and the topology optimization method of the multi-phase piezoelectric materials and pattern gradient constraint for piezoelectric energy harvesting structure is studied.This paper focuses on the optimization of piezoelectric conversion efficiency,multi-phase material performance,good manufacturability and high efficient solution,the main work is as follows:Firstly,the piezoelectric coupling analysis based on finite element method is studied.The piezoelectric coupling equilibrium equation of two-dimensional plane problem is deduced,and the finite element model is constructed.The distribution of the parameters under certain boundary conditions is obtained by an example which can validate the proposed methods.Secondly,an optimum design method of piezoelectric energy harvesting structure based on parametric level set(CSRBF)is proposed.A CSRBF is used to interpolate the level set function and the optimization model with the maximization of piezoelectric conversion is constructed,then the sensitivity analysis of objective function and constraint condition is carried out based on shape derivative and adjoint method.The boundary integral strategy is improved to volume integral strategy,therefore the velocity field is naturally extended to the whole design domain,leading to a new generation of holes and avoiding the dependence on initialization,the problem is solved based OC algorithm.An example is implemented to demonstrate the effectiveness of the present method.Thirdly,an optimization method for multiphase materials of piezoelectric energy harvesting structure based on the piecewise constant level set(PCLSM)is proposed.A topological optimization model including elasticity,piezoelectricity and empty material is constructed after the PCLSM method being introduced.The sensitivity analysis is deduced,and the multi-material problem is solved based on AOS(additive operator splitting)algorithm.Three-phase material distribution is calculated through an example,and a better performance,smooth boundary,clear structure is obtained.Fifthly,an optimization method of piezoelectric energy harvesting structure with pattern gradient constraints is proposed.The method to deal with pattern gradient constraints based on MTOP(multi resolution topology optimization)is studied,then an optimized model with pattern gradient constraints is established for piezoelectric energy structures.The problem is solved based MMA(method of moving asymptotes)algorithm.A structure with better form of pattern gradient,good manufacturing potential,performance improved is obtained by the present method.Finally,the paper is summarized and the future research directions are prospected.