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Removing Non-Uniqueness in Symmetric Galerkin Boundary Element Method for Elastostatic Neumann Problems and its Application to Half-Space Problems

Published online by Cambridge University Press:  07 May 2020

Y. -Y. Ko Open the ORCID record for Y. -Y. Ko [Opens in a new window]
Y. -Y. Ko*
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan
*
*Corresponding author ([email protected])
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Abstract

When the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

Keywords

SGBEMNeumann problemnon-uniquenesshalf-space problem
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 6 , December 2020 , pp. 749 - 761
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

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