An Efficient Dimension-Adaptive Numerical Integration Method for Stochastic Dynamic Analysis of Structures with Uncertain Parameters

Abstract

This paper presents a novel dimension-adaptive numerical integration method for dynamic analysis of structures with stochastic parameters subjected to deterministic excitations. First, an efficient dimension-adaptive algorithm is proposed to detect the importance of each random parameter involved in the structural model, based on which the quadrature nodes used for numerical integration can be collocated more reasonably. Then, the Gaussian quadrature formulas are used to evaluate the structural response statistics. To further improve the robustness and efficiency of the proposed method, the dimension-adaptive integration is only used to calculate the structural displacement response statistics. The velocity and acceleration response statistics are further evaluated using the finite difference formulas based on the concept of stochastic difference. Such a strategy is especially attractive when evaluating the response statistics of the derivative processes requires more quadrature nodes than that of the original process. Finally, two numerical examples encountered in civil engineering, including a shear frame with stochastic parameters subjected to a seismic ground motion and an Euler beam with unidimensional stochastic field of material properties (discretized via the Karhunen–Loève expansion) subjected to a moving load are studied to illustrate the performance of the proposed method. Via the numerical results, the accuracy and efficiency of the proposed method are verified.