The topology optimization problem of a continuum structure is further investigated under the independent position uncertainties of multiple external loads, which are now described with an interval vector of uncertain‐but‐bounded variables. In this study, the structural compliance is formulated with the quadratic Taylor series expansion of multiple loading positions. As a result, the objective gradient information to the topological variables can be evaluated efficiently upon an explicit quadratic expression as the loads deviate from their ideal application points. Based on the minimum (largest absolute) value of design sensitivities, which corresponds to the most sensitive compliance to the load position variations, a two‐level optimization algorithm within the non‐probabilistic approach is developed upon a gradient‐based optimization method. The proposed framework is then performed to achieve the robust optimal configurations of four benchmark examples, and the final designs are compared comprehensively with the traditional topology optimizations under the loading point fixation. It will be observed that the present methodology can provide a remarkably different structural layout with the auxiliary components in the design domain to counteract the load position uncertainties. The numerical results also show that the present robust topology optimization can effectively prevent the structural performance from a noticeable deterioration than the deterministic optimization in the presence of load position disturbances.

中文翻译：

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加载位置具有多个独立不确定性的鲁棒拓扑优化

在多个外部载荷的独立位置不确定性的情况下，对连续体结构的拓扑优化问题进行了进一步研究，现在用不确定性但有界变量的区间矢量来描述该问题。在这项研究中，结构柔度由多个加载位置的泰勒级数展开式表示。结果，当载荷偏离其理想应用点时，可以根据显式二次表达式有效地评估拓扑变量的客观梯度信息。基于设计灵敏度的最小（最大绝对值）（对应于对负载位置变化的最敏感顺应性），在基于梯度的优化方法上开发了非概率方法中的两级优化算法。然后执行所提出的框架以实现四个基准示例的鲁棒的最佳配置，并将最终设计与在加载点固定下的传统拓扑优化进行全面比较。将观察到，本方法可以在设计领域中与辅助部件一起提供明显不同的结构布局，以抵消载荷位置的不确定性。数值结果还表明，与存在载荷位置扰动的确定性优化方法相比，当前的鲁棒拓扑优化方法可以有效地防止结构性能明显下降。最终设计在负载点固定下与传统拓扑优化进行了全面比较。将观察到，本方法可以在设计领域中与辅助部件一起提供明显不同的结构布局，以抵消载荷位置的不确定性。数值结果还表明，与存在载荷位置扰动的确定性优化方法相比，当前的鲁棒拓扑优化方法可以有效地防止结构性能明显下降。最终设计在负载点固定下与传统拓扑优化进行了全面比较。将观察到，本方法可以在设计领域中与辅助部件一起提供明显不同的结构布局，以抵消载荷位置的不确定性。数值结果还表明，与存在载荷位置扰动的确定性优化方法相比，当前的鲁棒拓扑优化方法可以有效地防止结构性能明显下降。