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Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models

机译：基于非概率可靠性的凸模型对几何非线性结构的拓扑优化

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This paper describes a non-probabilistic reliability-based topology optimization method for the design of continuum structures undergoing large deformations. The variation of the structural system is treated with the multi-ellipsoid convex model, which is a realistic description of the parameters being inherently uncertain-but-bounded or lacking sufficient probabilistic data. The formulation of the optimal design is established as a volume minimization problem with non-probabilistic reliability constraints on the geometrically nonlinear structural behaviour. In order to circumvent numerical difficulties in solving the nested double-loop optimization problem, a performance measure-based approach is employed to transform the constraint on the reliability index into one on the concerned performance. In conjunction with an efficient adjoint variable scheme for the sensitivity analysis of reliability constraints, the optimization problem is solved by gradient-based mathematical programming methods. Three numerical examples for the optimization design of planar structures are presented to illustrate the validity and applicability of the proposed method. The obtained optimal solutions show the importance of incorporating various uncertainties in the design problem. Moreover, it is also revealed that the geometrical nonlinearity needs to be accounted for to ensure satisfaction of the reliability constraints in the optimal design of structures with large deformation.
机译：本文介绍了一种基于非概率可靠性的拓扑优化方法，用于设计承受大变形的连续体结构。用多椭球凸模型处理结构系统的变化，这是对参数固有地不确定但有界或缺乏足够概率数据的现实描述。最佳设计的制定被确定为体积最小化问题，在几何非线性结构行为上具有非概率可靠性约束。为了解决解决嵌套双环优化问题的数值难题，采用了一种基于性能测度的方法，将对可靠性指标的约束转化为对相关性能的约束。结合有效的伴随变量方案进行可靠性约束的敏感性分析，通过基于梯度的数学编程方法解决了优化问题。给出了三个数值例子，说明了平面结构的优化设计方法的有效性和适用性。获得的最佳解决方案表明在设计问题中纳入各种不确定性的重要性。此外，还揭示了几何非线性需要考虑在内，以确保满足对大变形结构的最佳设计的可靠性约束。

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