Engineering structures are required to meet strength conditions to ensure engineering safety, where the maximum stress level of the structure mainly characterizes the structural strength. This study proposes an isogeometric topology optimization method for the local stress-constrained design. This method establishes an optimization model with volume fraction as the objective function and maximum von Mises stress as the constraint condition. The augmented lagrangian approach is introduced to ensure that the design results satisfy stress constraints locally. To increase the convergence rate of stress-constrained topology optimization, we develop a new stress constraint function, and compare it with the other two stress constraint functions proposed by previous research. Sensitivity analysis of the local stress-constraint and volume objective based on an isogeometric topology optimization framework is systematically derived. The design result is compared with the traditional global stress minimization design through typical numerical examples. In addition, this method is extended to the three-dimensional stress-constrained topology optimization design problem that has rarely been studied in the isogeometric-analysis-based topology optimization framework. Several typical numerical examples are presented to demonstrate the method’s effectiveness. It demonstrates that the proposed method inherits the merits of the exact geometry and high-order continuity between elements of isogeometric analysis and can effectively control the maximum von Mises stress level of structures, with a faster convergence rate.

中文翻译：

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具有局部应力约束设计的等几何拓扑优化方法


工程结构需要满足强度条件以保证工程安全，其中结构的最大应力水平主要表征结构强度。本研究提出了一种用于局部应力约束设计的等几何拓扑优化方法。该方法建立了一个优化模型，其中体积分数为目标函数，最大 von Mises 应力作为约束条件。引入增广拉格朗日方法以确保设计结果局部满足应力约束。为了提高应力约束拓扑优化的收敛速度，我们开发了一种新的应力约束函数，并将其与先前研究提出的其他两个应力约束函数进行了比较。系统推导了基于等几何拓扑优化框架的局部应力约束和体积目标的敏感性分析。通过典型的数值算例，将设计结果与传统的全局应力最小化设计进行了对比。此外，该方法还扩展到了在基于等几何分析的拓扑优化框架中很少研究的三维应力约束拓扑优化设计问题。提出了几个典型的数值示例来证明该方法的有效性。结果表明，所提出的方法继承了等几何分析单元之间精确几何和高阶连续性的优点，可以有效地控制结构的最大 von Mises 应力水平，具有更快的收敛速度。