A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty

Abstract

A non-intrusive approach coupled with non-uniform rational B-splines based isogeometric finite element method is proposed here. The developed methodology was employed to study the stochastic static bending and free vibration characteristics of functionally graded material plates with inhered material randomness. A first order shear deformation theory with an artificial shear correction factor was used for spatial discretization. The output randomness is represented by polynomial chaos expansion. The robustness and accuracy of the framework were demonstrated by comparing the results with Monte Carlo simulations. A systematic parametric study was carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol’ indices. Functionally graded plates made up of Aluminium (Al) and Zirconium Oxide (ZrO2) were considered in all the numerical examples.

Global sensitivity analysis of parameters based on sPCE: The case study of a concrete face rockfill dam in northwest China

“…At present, PCE has been successfully applied to sensitivity analysis in different fields [12][13][14][15][16][17], and its techniques can be mainly divided into the invasive method and the non-invasive method [18]. The former is put forward under the background of the stochastic finite element method, which is used to discretize constitutive equations in physical space and random space; the latter is based on post-processing multiple analog outputs of existing numerical models [19,20]. Compared with the invasive method, the non-invasive method is simple to use and easy to solve, so it has a wider scope of application.…”