Hybrid analytical technique for nonlinear analysis of structures

Abstract

A two-step hybrid analytical technique is presented for predicting the nonlinear response of structures. The technique is based on the successive application of the regular perturbation expansion and either the method of weighted residuals or the classical direct variational technique. The functions associated with the various-order terms in the perturbation expansion of the fundamental unknowns are first obtained by using the regular perturbation method. These functions are selected as coordinate functions (or modes) and either the weighted residuals or the classical direct variational method of technique is then used to compute their amplitudes. The potential of the proposed hybrid technique for nonlinear analysis of structures is discussed. The effectiveness of this technique is demonstrated by means of three numerical examples. Results of the study indicate that the hybrid technique overcomes two major drawbacks of the parent (classical) techniques: 1) the requirement of using a small parameter in the regular perturbation method, and 2) the arbitrariness in the choice of the coordinate functions in both the weighted residual and the direct variational techniques. Therefore, the proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of both the method of weighted residuals and the direct variational technique.