Overestimation Analysis of Interval Finite Element for Structural Dynamic Response

Abstract

Dynamic response analysis plays an important role for the structural design. For engineering structures, there exist model inaccuracies and structural parameters uncertainties. Consequently, it is necessary to express these uncertain parameters as interval variables and introduce the interval finite element method (IFEM), in which the elements in stiffness matrix, mass matrix and damping matrix are all the function of interval parameters. The dependence of interval parameters leads to overestimation of dynamic response analysis. In order to reduce the overestimation of IFEM, the element-based subinterval perturbation for static analysis is applied to dynamic response analysis. According to the interval range, the interval parameters are divided into different subintervals. With permutation and combination of each subinterval, the upper and lower bounds of displacement response are obtained. Because of the large number of degrees of freedom and uncertain parameters, the Laplace transform is used to evaluate the dynamic response for avoiding to frequently solve the interval finite element linear equations. The numerical examples illustrate the validity and feasibility of the proposed method.