The solution to an elliptic partial differential equation for facilitating exact volume integral transformation in the 3D BEM analysis

Y. C. Shiah, Meng Rong Li

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In the direct boundary element method (BEM), the body-force or its equivalence will reveal itself as a volume integral that shall destroy the important notion of boundary discretisation. For resolving this issue, the most elegant approach would be to analytically transform the volume integral to boundary ones. In the process of such attempt for 3D anisotropic elastostatics, the key lies in analytically formulating the fundamental solution to a partial differential equation. In this paper, the partial differential equation is presented in an elliptic form, followed by formulating its analytical solution. In the BEM analysis, the formulated solution will be a key part to the success of performing exact volume-to-surface integral transformation.

Original languageEnglish
Pages (from-to)13-18
Number of pages6
JournalEngineering Analysis with Boundary Elements
Volume54
DOIs
Publication statusPublished - 2015 May

Fingerprint

Integral Transformation
Elliptic Partial Differential Equations
Boundary element method
Boundary Elements
Partial differential equations
Partial differential equation
Elasticity
Surface integral
Elastostatics
Fundamental Solution
Analytical Solution
Discretization
Equivalence
Transform

All Science Journal Classification (ASJC) codes

  • Analysis
  • Engineering(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{ab54b8bd948740429f40b5462556a9a7,
title = "The solution to an elliptic partial differential equation for facilitating exact volume integral transformation in the 3D BEM analysis",
abstract = "In the direct boundary element method (BEM), the body-force or its equivalence will reveal itself as a volume integral that shall destroy the important notion of boundary discretisation. For resolving this issue, the most elegant approach would be to analytically transform the volume integral to boundary ones. In the process of such attempt for 3D anisotropic elastostatics, the key lies in analytically formulating the fundamental solution to a partial differential equation. In this paper, the partial differential equation is presented in an elliptic form, followed by formulating its analytical solution. In the BEM analysis, the formulated solution will be a key part to the success of performing exact volume-to-surface integral transformation.",
author = "Shiah, {Y. C.} and Li, {Meng Rong}",
year = "2015",
month = "5",
doi = "10.1016/j.enganabound.2014.12.011",
language = "English",
volume = "54",
pages = "13--18",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - The solution to an elliptic partial differential equation for facilitating exact volume integral transformation in the 3D BEM analysis

AU - Shiah, Y. C.

AU - Li, Meng Rong

PY - 2015/5

Y1 - 2015/5

N2 - In the direct boundary element method (BEM), the body-force or its equivalence will reveal itself as a volume integral that shall destroy the important notion of boundary discretisation. For resolving this issue, the most elegant approach would be to analytically transform the volume integral to boundary ones. In the process of such attempt for 3D anisotropic elastostatics, the key lies in analytically formulating the fundamental solution to a partial differential equation. In this paper, the partial differential equation is presented in an elliptic form, followed by formulating its analytical solution. In the BEM analysis, the formulated solution will be a key part to the success of performing exact volume-to-surface integral transformation.

AB - In the direct boundary element method (BEM), the body-force or its equivalence will reveal itself as a volume integral that shall destroy the important notion of boundary discretisation. For resolving this issue, the most elegant approach would be to analytically transform the volume integral to boundary ones. In the process of such attempt for 3D anisotropic elastostatics, the key lies in analytically formulating the fundamental solution to a partial differential equation. In this paper, the partial differential equation is presented in an elliptic form, followed by formulating its analytical solution. In the BEM analysis, the formulated solution will be a key part to the success of performing exact volume-to-surface integral transformation.

UR - http://www.scopus.com/inward/record.url?scp=84922247130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922247130&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2014.12.011

DO - 10.1016/j.enganabound.2014.12.011

M3 - Article

AN - SCOPUS:84922247130

VL - 54

SP - 13

EP - 18

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

ER -