Currently, due to the complexity of multi-scale topology optimization (MSTO), most of them are optimized based on deterministic conditions, ignoring the influence of uncertain factors on multi-scale structural design optimization. This article aims to develop a novel approach to probabilistic reliability-based topology optimization of multi-scale structure (RBTOM) to address the optimization design problem considering external loading uncertainties. Firstly, the level set function (LSF) is used to represent the geometric shape of the lattice micro-structure, and the optimization parameters are defined. Secondly, an offline database is established based on the numerical homogenization to obtain the equivalent stiffness matrix of the structure. Then, a minimum relative volume fraction nested two-layer iterative algorithm that meets the target reliability requirements is established. The inner layer is based on the reliability analysis of the reliability index approach (RIA), and the outer layer is used for coarse-scale topology optimization, and then reconstructed based on the optimization results. Finally, the effectiveness of the proposed method is illustrated by two examples of different level set functions.

中文翻译：

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载荷不确定性下基于概率可靠性的多尺度结构拓扑优化


目前，由于多尺度拓扑优化 （MSTO） 的复杂性，大多数拓扑优化都是基于确定性条件进行优化的，忽略了不确定因素对多尺度结构设计优化的影响。本文旨在开发一种新的基于概率可靠性的多尺度结构拓扑优化 （RBTOM） 方法，以解决考虑外部加载不确定性的优化设计问题。首先，使用水平集函数 （LSF） 表示晶格微观结构的几何形状，并定义优化参数;其次，基于数值均质化建立离线数据库，得到结构的等效刚度矩阵;然后，建立满足目标可靠性要求的最小相对体积分数嵌套两层迭代算法。内层基于可靠性指数法 （RIA） 的可靠性分析，外层用于粗尺度拓扑优化，然后根据优化结果进行重构。最后，通过两个不同水平集函数的例子说明了所提出的方法的有效性。