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.

基于独立连续映射方法，提出了一种连续体结构的几何非线性拓扑优化方法。由于结构强度在工程应用中的重要性，因此对应力约束问题进行了研究。首先，建立了以单元应力为约束的轻量化结构的拓扑优化模型。其次，采用应力全球化方法将局部应力约束转换为应变能约束，克服了局部应力约束所引起的模型建立，灵敏度分析和大量求解计算等难题。第三，分析了目标函数和约束函数的敏感性，并采用渐近渐近线的方法求解了优化模型。此外，利用加性超弹性技术解决结构大变形引起的数值不稳定性。数值算例验证了该方法的可行性。该方法为几何非线性优化设计提供了重要参考。