Geometrically Nonlinear Topology Optimization of Continuum Structures Based on an Independent Continuous Mapping Method  

作　　者：Hong-ling Ye Bo-shuai Yuan Ji-cheng Li Xing Zhang Yun-kang Sui 

机构地区：[1]Faculty of Materials and Manufacturing,Beijing University of Technology,Beijing,100124,China

出　　处：《Acta Mechanica Solida Sinica》2021年第5期658-672,共15页固体力学学报（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(11872080);Beijing Natural Science Foundation(3192005)。

摘　　要：A geometrically nonlinear topology optimization method for continuum structures is proposed based on the independent continuous mapping method.The stress constraint problem is studied due to the importance of structural strength in engineering applications.First,a topology optimization model is established for a lightweight structure with element stress as constraints.Second,the stress globalization method is adopted to convert local stress constraints into strain energy constraints,which overcomes the difficulties caused by local stress constraints,such as model establishment,sensitivity analysis,and massive solution calculations.Third,the sensitivity of the objective function and constraint function is analyzed,and the method of moving asymptotes is employed to solve the optimization model.In addition,the additive hyperelasticity technique is utilized to solve the numerical instability induced by structures undergoing large deformation.Numerical examples are given to validate the feasibility of the proposed method.The method provides a significant reference for geometrically nonlinear optimization design.

关 键 词：Topology optimization Geometric nonlinearity ICM method Stress constraints Stress globalization 

分 类 号：O344.1[理学—固体力学]