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Stress-constrained topology optimization with design-dependent loading

机译：应力约束的拓扑优化与设计相关的加载

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摘要

The purpose of this paper is to apply stress constraints to structural topology optimization problems with design-dependent loading. A comparison of mass-constrained compliance minimization solutions and stress-constrained mass minimization solutions is also provided. Although design-dependent loading has been the subject of previous research, only compliance minimization has been studied. Stress-constrained mass minimization problems are solved in this paper, and the results are compared with those of compliance minimization problems for the same geometries and loading. A stress-relaxation technique is used to avoid the singularity in the stress constraints, and these constraints are aggregated in blocks to reduce the total number of constraints in the optimization problem. The results show that these design-dependent loading problems may converge to a local minimum when the stress constraints are enforced. The use of a continuation method where the stress-constraint aggregation parameter is gradually increased typically leads to better convergence; however, this may not always be possible. The results also show that the topologies of compliance-minimization and stress-constrained solutions are usually vastly different, and the sizing optimization of a compliance solution may not lead to an optimum.
机译：本文的目的是将应力约束应用于具有设计相关载荷的结构拓扑优化问题。还提供了质量受约束的最小化解决方案和应力受约束的最小化解决方案的比较。尽管依赖设计的加载已成为先前研究的主题，但仅研究了合规性最小化。解决了应力约束的质量最小化问题，并将结果与​​相同几何形状和相同载荷下的柔性最小化问题进行了比较。应力松弛技术用于避免应力约束中的奇异性，并且将这些约束汇总为块，以减少优化问题中的约束总数。结果表明，当实施应力约束时，这些与设计有关的载荷问题可能会收敛到局部最小值。逐渐增加应力约束聚集参数的连续方法的使用通常会导致更好的收敛；但是，这并不总是可能的。结果还表明，合规性最小化和受压力约束的解决方案的拓扑通常差异很大，并且合规性解决方案的大小优化可能不会导致最优。

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