The present study proposes a method of robust topology optimization assuming uncertainties in the magnitude and direction of loads applied to a geometrically nonlinear structure. The objective function is the sum of the expected value and the standard deviation of end‐compliance of a structure with a compressible Neo‐Hookean hyperelasticity. In this study, quadratic approximation of the end‐compliance with respect to random variables is employed to reduce computational cost. To ensure its accuracy, a complete analytical formulation is derived, and the performance and limitation of the proposed method are deeply discussed. The performance of the proposed method is verified and its numerical examples emphasize the importance of considering geometrical nonlinearity to obtain robust structures with respect to uncertainties of loading conditions. Finally, we have obtained a finding that the optimized network system consisting of thin members plays a significant role in the improvement of robustness of structures.

中文翻译：

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考虑不确定载荷条件的基于有限应变的鲁棒拓扑优化

本研究提出了一种鲁棒拓扑优化的方法，该方法假设应用于几何非线性结构的载荷的大小和方向具有不确定性。目标函数是具有可压缩的新霍克超弹性结构的预期值与端部柔顺度标准偏差之和。在这项研究中，对随机变量的末端一致性的二次逼近被用来减少计算成本。为了确保其准确性，导出了完整的分析公式，并对所提方法的性能和局限性进行了深入讨论。验证了所提方法的性能，其数值示例强调了考虑几何非线性来获得关于载荷条件不确定性的鲁棒结构的重要性。