New Discretization Methodology for Three-Dimensional Mechanical Parameters Considering Spatial Variations

Abstract

In this paper, the uncertain mechanical parameters are modeled as spatial random fields (RFs). A new tetrahedral discretization methodology of three-dimensional (3D) RF is proposed based on the local average (LA) theory. An analytical formula and a numerical formula of the covariance for any two tetrahedral RF elements are developed. Its main advantage, compared to similar studies employing hexahedral discretization method, is that tetrahedral LA method can perfectly combine with tetrahedral finite element (FE) method. Also, the corresponding relation between RF mesh and FE mesh is clearer and the computer codes are simpler. The accuracy of proposed LA method in this study was verified by comparing with other discretization techniques of RF. Finally, an illustrative example is presented to demonstrate the analysis process. The validity and the advantage of the proposed LA method are proven. Taking the spatial variations of uncertain mechanical parameters into account, the stochastic effects of scale of fluctuation on the RF are estimated. The proposed method can be widely applied to 3D stochastic FE analysis, and the sample results will improve our understanding of the stochastic influence of scale of fluctuation on the RF.