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IGA-SIMP method based stress-constrained topology optimization of continuum structures

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 作者 单位 E-mail 刘宏亮 大连理工大学 杨迪雄 大连理工大学力学系 yangdx@dlut.edu.cn

本文建立了一种IGA-SIMP框架下的连续体结构应力约束拓扑优化方法。基于常用的SIMP模型，将非均匀有理B样条（NURBS）函数用于几何建模、结构分析和设计参数化，实现了结构分析和优化设计的集成统一。利用高阶连续的NURBS基函数，等几何分析（IGA）提高了结构应力及其灵敏度的计算精度，加强了拓扑优化结果的可信性。为处理大量局部应力约束，提出了基于稳定转换法修正的P-norm应力约束策略，以克服拓扑优化中的迭代振荡和收敛性困难。几个典型的平面应力问题拓扑优化算例表明了本文方法的有效性和精确性。应力约束下的体积最小化设计以及体积和应力约束下的柔顺度最小化设计的算例表明，基于稳定转换法修正的约束策略可以抑制应力约束体积最小化设计中的迭代振荡现象，获得稳定收敛的优化解；比较而言，体积和应力约束下的柔顺度最小化设计的迭代过程更加稳健，适合采用精确修正的应力约束策略。

This paper establishes an isogeometric analysis (IGA)-SIMP method for the stress-constrained topology optimization of continuum structures. Based on the popular SIMP model, the unified NURBS (non-uniform rational B-spline) function is utilized for geometry modeling, structure analysis and design parameterization, which can well integrate structure analysis with optimization design. By virtue of high-order continuous NURBS basis functions, the isogeometric analysis improves the computational accuracy of stress and its sensitivities, and thus enhances the credibility of optimization results. For handling the numerous local stress constraints, a STM (stability transformation method) correction-based P-norm stress constraint strategy is proposed to overcome the iteration oscillation and convergence difficulty of topology optimization problem. Several representative topology optimization examples of 2D plane stress problem illustrate the effectiveness and accuracy of the present design method. Numerical examples, including the stress-constrained volume minimization design and the mean compliance minimization design with the constraints of both volume and stress, indicate that the STM-based stress correction strategy is able to suppress the iterative oscillation in volume minimization design problem and realize stable convergence. By comparison, the optimization iterations for the mean compliance minimization design with the constraints of both volume and stress are more stable, and thus the exact stress correction strategy is suitable for addressing this issue.
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