Boundary-Element Modeling of 3-D Poroelastic Half-Space Dynamics

2014 ◽  
Vol 1040 ◽  
pp. 881-885 ◽  
Author(s):  
Leonid A. Igumnov ◽  
Svetlana Litvinchuk ◽  
Andrey Petrov ◽  
Alexander A. Belov
Keyword(s):  
Boundary Element Method ◽  
Boundary Value Problems ◽  
Boundary Element ◽  
Half Space ◽  
Material Model ◽  
Direct Approach ◽  
Computational Results ◽  
Element Modeling ◽  
Base Functions ◽  
Space Dynamics

A direct approach of the boundary element method for treating 3-D boundary-value problems of poroelastodynamics is considered. Biot’s material model with four unknown base functions is used. Computational results for the surface responses of displacements and pore pressures as functions of a force acting on a half-space weakened by a cavity are presented.

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

2020 ◽  
Vol 36 (6) ◽  
pp. 749-761
Author(s):  
Y. -Y. Ko
Keyword(s):  
Boundary Element Method ◽  
Rigid Body ◽  
Boundary Element ◽  
Integral Equations ◽  
Half Space ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Neumann Problems ◽  
Galerkin Boundary Element Method ◽  
Element Method

ABSTRACTWhen 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.

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