Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

Abstract

In this paper, based on the second-order Taylor series expansion and the difference of convex functions algorithm for quadratic problems with box constraints (the DCA for QB), a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods. Although the first-order parameter perturbation method (FM) is effective for solving the static response problem of structures with interval parameters with small uncertainties, the method may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, a new approach (the proposed method:PM) is presented based on the second-order Taylor series expansion and the DCA for QB(the difference of convex functions algorithm for quadratic problems with box constraints).