This paper proposes an interval finite element method based on function decomposition for structural static response problems with large-scale unknown-but-bounded parameters. When there is a large number of uncertain parameters, it will lead to the curse of dimensionality. The existing Taylor expansion-based methods, which is often employed to deal with large-scale uncertainty problems, need the sensitivity information of response function to uncertain parameters. However, the gradient information may be difficult to obtain for some complicated structural problems. To overcome this drawback, univariate decomposition expression (UDE) and bivariate decomposition expression (BDE) are deduced by the higher-order Taylor series expansion. The original structure function with n-dimensional interval parameters is decomposed into the sum of several low-dimensional response functions by UDE or BDE, each of which has only one or two interval parameters while the other interval parameters are replaced by their midpoint values. Therefore, solving the upper and lower bounds of the n-dimensional function can be converted into solving those of the one- or two-dimensional functions, which savethe calculation costs and can be easily implemented. The accuracy and efficiency of the new method are verified by three numerical examples.

中文翻译：

---

大尺度未知但有界参数不确定结构的静力响应分析

提出了一种基于函数分解的区间有限元方法，用于求解大规模参数未知但有界的结构静力响应问题。当存在大量不确定参数时，就会导致维数灾难。现有的基于泰勒展开的方法常用于处理大规模不确定性问题，需要响应函数对不确定参数的敏感性信息。然而，对于一些复杂的结构问题，梯度信息可能难以获得。为了克服这个缺点，单变量分解表达式（UDE）和双变量分解表达式（BDE）由高阶泰勒级数展开推导。原始结构函数n维区间参数通过UDE或BDE分解为几个低维响应函数的总和，每个低维响应函数只有一个或两个区间参数，而其他区间参数被它们的中点值代替。因此，求解上界和下界n可以将一维函数转化为求解一维或二维函数，节省计算成本，易于实现。通过三个数值算例验证了新方法的准确性和有效性。