The stochastic Galerkin scaled boundary finite element method on random domain

Abstract

Summary The research work extends the scaled boundary finite element method to non‐deterministic framework defined on random domain wherein random behaviour is exhibited in the presence of the random‐field uncertainties. The aim is to blend the scaled boundary finite element method into the Galerkin spectral stochastic methods, which leads to a proficient procedure for handling the stress singularity problems and crack analysis. The Young's modulus of structures is considered to have random‐field uncertainty resulting in the stochastic behaviour of responses. Mathematical expressions and the solution procedure are derived to evaluate the statistical characteristics of responses (displacement, strain, and stress) and stress intensity factors of cracked structures. The feasibility and effectiveness of the presented method are demonstrated by particularly chosen numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

A scaled boundary finite element partitioning based reduced order algorithm for the elastic analysis of cyclically symmetric structures

“…The rotationally symmetric structure with a common node Substituting Equations ( 19) and (20) into Equation (18) yields…”

“…11,12 By combining with quadtree/octree gridding techniques, the SBFE mesh generation becomes more efficient, and can even be directly conducted on the digital images of computing domains. 13,14 Due to these merits, such a kind of SBFEM has been used to deal with dynamic problems, 15,16 heat conduction problem, 17,18 uncertainty problem, 19,20 inverse problem. 21 Either in the appearance of BEM or FEM, however, a troublesome matter for SBFEM is the computational expense on solving a quadratic eigenvalue problem in generating stiffness matrix.…”

“…By combining with quadtree/octree gridding techniques, the SBFE mesh generation becomes more efficient, and can even be directly conducted on the digital images of computing domains 13,14 . Due to these merits, such a kind of SBFEM has been used to deal with dynamic problems, 15,16 heat conduction problem, 17,18 uncertainty problem, 19,20 inverse problem 21 …”

Eigenvibrations of Kirchhoff Rectangular Random Plates on Time-Fractional Viscoelastic Supports via the Stochastic Finite Element Method

“…A coupled FEM-BEM-least squares point interpolation for a structure-acoustic system with a stochastic perturbation technique was proposed by Zhang et al [8]. The stochastic Galerkin scaled boundary finite element approach was proposed by Duy Mihh et al [9] for the randomly defined domain. The Monte Carlo simulation technique coupled with the scaled boundary FEM was applied by Chowdhury et al [10] for probabilistic fracture mechanics.…”

Stochastic Vibrations of a System of Plates Immersed in Fluid Using a Coupled Boundary Element, Finite Element, and Finite Difference Methods Approach

“…A coupled Finite and Boundary Element Method linked with the least squares point interpolation approach coupled with the stochastic perturbation method for a structure-acoustic system have been investigated by Zang et al [34]. Another research branch is the stochastic extension of the scaled Boundary Finite Element Method [35][36][37] provided according to the Karhunen-Loeve expansion and the Monte Carlo simulation (MCS). Comparatively, the SPT technique allows for an approximate solution to the boundary value problem that cannot be accurately treated [38,39].…”