针对含有界但未知不确定性的结构静力响应问题，提出了一种单变量函数分解的区间有限元法。首先，将区间有限元的位移函数在单变量点处进行高阶 Taylor 展开， 推导出其单变量函数分解区间表达式。然后，利用单变量区间函数分解，将 n 维位移函 数近似表达为 n 个一维函数的和函数，每个一维函数有且仅有 1 个区间参数，其余区间 参数被它们的区间中点代替。由此，将 n 维函数上、下界的求解问题转换为求解一维函 数的上、下界，计算成本降低且易于实现。与现有的区间摄动有限元法相比，该方法不需要计算位移函数对不确定变量的灵敏度，且不需要计算结构刚度矩阵的逆，并适合求解强非线性的响应函数。数值算例结果表明文中方法是有效可行的。

An interval finite element method based on univariate function decomposition was proposed to deal with the problem of the static response with unknown-but-bounded uncertainties． Firstly，the displacement function of interval finite element was expanded by higher-order Taylor series at the single variable points，and the interval expression of univariate function decomposition is derived． An n-dimension displacement function is approximately expressed as the sum function of n one-dimension functions by using the univariate interval function decomposition． Each one-dimension function has only one interval parameter，and the rest of the interval parameters are replaced by their interval midpoint． Thus，the problem of solving the upper and lower bounds of n-dimension function can be converted to solving that of one-dimension functions，which reduces the computational cost and is easy to implement． Compared with the existing interval perturbation finite element method，the proposed method does not need to calculate the sensitivity of the response to the uncertain variables and the inverse of the structural stiffness matrix， and is suitable for solving the strongly nonlinear response function． The numerical results show that this method is effective and feasible．