Stochastic isogeometric analysis method for plate structures with random uncertainty

Abstract

This paper proposes the stochastic isogeometric analysis (IGA) method in conjunction with the perturbation technique for random response analysis of plate structures. Specifically, the benchmark solutions of stochastic deflection responses for rectangular plate are achieved. Firstly, the random field is represented by Karhunen-Loève expansion, and the corresponding analytical formulas of the Fredholm integral equation for rectangular plate are illustrated to obtain the benchmark stochastic responses. Subsequently, the stochastic IGA framework is suggested by combining isogeometric analysis with the first-order perturbation technique, especially for the bending problems of circular Mindlin plates and Kirchhoff plates. Moreover, the first two moments of stochastic responses of plate structures are formulated. Finally, the efficiency and applicability of the stochastic IGA method are demonstrated by three numerical examples. To compare with the efficiency and accuracy of proposed method, the mean values, standard deviations and coefficients of variation of stochastic responses are calculated by Monte Carlo simulation. For the rectangular and circular Kirchhoff thin plates, the effects of different correlation lengths, boundary conditions and loading cases on stochastic responses and uncertainty propagation are scrutinized. It is also indicated that the proposed stochastic IGA method presents high efficiency and acceptable accuracy of random structural analysis of plates.