关键词: 结构静力响应, 区间有限元, 区间参数, 单变量函数分解, Taylor 展开

Abstract: 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．

Key words: structural static response, interval finite element, interval parameter, univariate function decomposition, Taylor series expansion