Abstract This paper proposes a semi-analytical interval method for static response bounds analysis of structures subjected to spatially uncertain loads. In the investigated problem, the external loads applied to the structure are spatially uncertain but bounded, which are quantified by an interval field model using upper and lower bounds. By introducing the interval field and its series expansion form into finite element analysis, the interval finite element equilibrium equations are then formulated, where the force vector is an interval vector. Solving the interval equations by the proposed method, a semi-analytical solution of the upper and lower bounds of structural static responses such as displacement and stress can be obtained efficiently. Finally, the effectiveness and accuracy of the proposed method are verified by three numerical examples.

中文翻译：

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空间不确定载荷结构响应界分析的半解析区间法

摘要 本文提出了一种半解析区间法，用于空间不确定荷载作用下结构的静态响应边界分析。在所研究的问题中，施加到结构上的外部载荷在空间上是不确定的但有界，这是通过使用上下界的区间场模型来量化的。将区间场及其级数展开形式引入有限元分析，得到区间有限元平衡方程，其中力向量为区间向量。用所提出的方法求解区间方程，可以有效地得到结构静力响应如位移和应力的上下界的半解析解。最后，通过三个数值算例验证了所提方法的有效性和准确性。