This paper proposes a stress-constrained structural topology optimization method in the velocity field level set framework. To avoid the strength failure in structures, the stress should meet certain strength criteria at all material points. This point-wise constraint brings great difficulty to topology optimization. Instead of using the traditional aggregation scheme, we propose a new stress constraint in the single domain integral form, which is mathematically equivalent to the point-wise stress limitation and enables the precise stress control throughout the entire material domain without introducing numerous constraints. Its simple expression with relatively low non-linearity facilitates the optimization formulation, the sensitivity analysis and the numerical implementation. Here, the velocity field level set method is used for the stress-constraint topology optimization. The implicit material representation by the level set model is combined with the body-fitted mesh, which provides a clear and smooth material boundary with high numerical calculation accuracy for the stress and the sensitivity. Moreover, the velocity field level set method maps the original boundary variation-based optimization problem from the functional design space into a finite-dimensional one by introducing the velocity field design variables. Thus, it allows using of the general mathematical optimization algorithms in the level set model, which provides an efficient and steady way to deal with the stress-constrained optimization problems.

中文翻译：

---

使用速度场能级集方法的应力约束拓扑优化


该文在速度场能级集框架中提出了一种应力约束结构拓扑优化方法。为避免结构中的强度失效，应力应在所有材料点上满足一定的强度标准。这种逐点约束给拓扑优化带来了很大的难度。我们提出了一种新的单域积分形式的应力约束，而不是使用传统的聚合方案，它在数学上等价于逐点应力限制，并且可以在整个材料域中实现精确的应力控制，而无需引入大量约束。其表达式简单，非线性度相对较低，有利于优化公式、灵敏度分析和数值实现。在这里，速度场水平集方法用于应力-约束拓扑优化。水平集模型的隐式材料表示与体拟合网格相结合，为应力和灵敏度提供了清晰光滑的材料边界，具有很高的数值计算精度。此外，速度场能级集方法通过引入速度场设计变量，将原始基于边界变化的优化问题从函数设计空间映射到有限维优化问题。因此，它允许在水平集模型中使用通用数学优化算法，这为处理应力约束优化问题提供了一种有效且稳定的方法。