Static stiffness of rigid foundation resting on elastic half-space using a Galerkin boundary element method

2020 ◽  
Vol 225 ◽  
pp. 111061
Author(s):  
Daniele Baraldi ◽  
Nerio Tullini
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Half Space ◽  
Elastic Half Space ◽  
Rigid Foundation ◽  
Static Stiffness ◽  
Galerkin Boundary Element Method ◽  
Element Method

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.

scholarly journals Boundary element method for nonadhesive and adhesive contacts of a coated elastic half-space

2019 ◽  
Vol 234 (1) ◽  
pp. 73-83 ◽  
Author(s):  
Qiang Li ◽  
Roman Pohrt ◽  
Iakov A Lyashenko ◽  
Valentin L Popov
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Half Space ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
Fourier Space ◽  
Numerical Tests ◽  
New Formulation ◽  
Adhesive Contacts ◽  
Element Method

We present a new formulation of the boundary element method for simulating the nonadhesive and adhesive contact between an indenter of arbitrary shape and an elastic half-space coated with an elastic layer of different material. We use the Fast Fourier Transform-based formulation of boundary element method, while the fundamental solution is determined directly in the Fourier space. Numerical tests are validated by comparison with available asymptotic analytical solutions for axisymmetric flat and spherical indenter shapes.

scholarly journals Direct boundary element method for dynamics in a half-space

1993 ◽  
Vol 83 (5) ◽  
pp. 1373-1390
Author(s):  
Paul S. Nowak ◽  
John F. Hall
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Half Space ◽  
Singular Integral Equations ◽  
Elastic Half Space ◽  
Resonance Phenomenon ◽  
Additional Source ◽  
Artificial Damping ◽  
Direct Boundary Element Method ◽  
Element Method

Abstract An application of the direct boundary element method for solving the response of a linearly elastic half-space with a canyon cut into the surface is presented. This approach uses source solutions for an undamped half-space where the resulting singular integral equations are solved directly without adding any artificial damping. Solutions for the displacements on the canyon surface reveal an artificial resonance phenomenon when solving the exterior problem in the frequency domain. The use of an additional source loading in the boundary element method is shown to eliminate these resonances and yield accurate results. A method for solving the Rayleigh waves generated on the surface of the half-space caused by the canyon is shown.

Sign in / Sign up

Export Citation Format

Share Document