形状记忆合金结构拓扑优化设计方法研究

Shape memory alloy (SMA) has drawn wide attention due to its excellent mechanical properties, and has been innovatively applied in many fields. In order to improve mechanical properties of SMA structures, a topology optimization method based on solid isotropic materials with penalization (SIMP) was proposed. The ZM model was adopted, and the elastic modulus of austenite and martensite as well as the phase change yield stresses of intermediate density materials introduced during the topology optimization process are interpolated. In order to obtain accurate mechanical responses, the material nonlinearity effect and geometric nonlinearity effect are considered. The three-field scheme are used to avoid checkerboarding patterns, mesh-dependency issues and intermediate density elements in the final results. The super element method is used to avoid the numerical instability caused by low density elements in nonlinear finite element analysis. Sensitivities are calculated via adjoint method. Finally, 2D and 3D numerical examples are presented to demonstrate the effectiveness of the proposed optimization method. The results show that the SMA structures with expected performance can be designed by the topology optimization framework proposed in this paper.