Research On Macrostructure Design Method For SMA Materials

Shape Memory Alloys(SMA)have many unique mechanical properties,such as superelasticity and shape memory effect,thus they are widely used in various engineering fields.However,the structural topology of SMA is generally relatively simple(mostly wire,bar,plate,etc.),which limits the performance of SMA to a certain extent.As the conceptual design stage of structural design,topology optimization is decisive for the effectiveness of the structure.The existing topology optimization research is mainly based on linear material and small deformation analysis.For SMA materials,besides the material’s constitutive model is nonlinear,its structural deformation usually also exhibits geometric nonlinearity.In this paper,in order to extend the structural design method of SMA and provide a basis for the structural optimization and high-performance structural design of SMA,a topology optimization algorithm for SMA material is established under the premise of considering the nonlinearity of material constitutive relation and geometric nonlinearity.The main contents of the thesis are as follows:Firstly,the SMA superelasticity is analyzed by the finite element analysis software ANSYS.By comparing with the experimental results,the reliability of the superelasticity simulation results is proved.In addition,the defects of the ANSYS superelasticity module in the simulation of the mechanical behavior of the SMA in the martensitic state are pointed out.Secondly,on the basis of the simulation work,the structure topology optimization design algorithm of SMA material is studied.The SIMP model is used to describe the topology optimization problem and the model is solved by gradient algorithm.The sensitivity information required by the gradient algorithm is deduced by constructing the Lagrangian function,and when the optimization objective is a displacement field function,the basic derivation method of the objective sensitivity is summarized.Since this topology optimization problem is based on nonlinear analysis,a semi-analytical solution of the adjoint vector is proposed to solve its sensitivity,which reduces the workload of sensitivity calculation.After that,for the numerical instability phenomena which are shown in the topology optimization design based on the SIMP model of SMA material structure,the corresponding elimination or improvement method are proposed.In order to eliminate the checkerboard and mesh dependence in the optimization results,the sensitivity filter based on Helmholtz-type partial differential equation is adopted;for the gray-scale elements problem,the Heaviside projection technology is introduced to binarize the pseudo-density distribution of the elements and reduce the number of intermediate density elements;for the mesh distortion problem of low-density elements in nonlinear finite element analysis based on SIMP model,the mesh deformation index constraint function and an additive hyperelasticity technique which based on second-order yeoh model are given.The topology optimization of cantilever beam structure and spaceborne membrane microstrip reflectarry antenna are given respectively to demonstrate the effectiveness of the proposed algorithm.Finally,based on the discussion results,a relatively complete nonlinear topology optimization system based on SIMP model for SMA superelasticity is established.The influence of material nonlinearity and geometric nonlinearity on the optimization results is investigated.At the same time,through a numerical example,the influence of the selection method of Heaviside projection function parameters on the optimization result is discussed,which provides a reference for the subsequent optimization work.