scholarly journals A local point interpolation method for static and dynamic analysis of thin beams

2001 ◽  
Vol 190 (42) ◽  
pp. 5515-5528 ◽  
Author(s):  
Y.T. Gu ◽  
G.R. Liu
Keyword(s):  
Dynamic Analysis ◽  
Interpolation Method ◽  
Static And Dynamic Analysis ◽  
Local Point ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Thin Beams

Coupling BEM and the Local Point Interpolation for the Solution of Anisotropic Elastic Nonlinear, Multi-Physics and Multi-Fields Problems

2019 ◽  
Vol 17 (09) ◽  
pp. 1950067
Author(s):  
Richard Kouitat Njiwa ◽  
Gael Pierson ◽  
Arnaud Voignier
Keyword(s):  
Solid Mechanics ◽  
Interpolation Method ◽  
Nonlinear Problems ◽  
Numerical Approach ◽  
Local Point ◽  
Problem Dimension ◽  
Point Interpolation Method ◽  
Elasticity Problems ◽  
Point Interpolation ◽  
Anisotropic Elastic

The pure boundary element method (BEM) is effective for the solution of a large class of problems. The main appeal of this BEM (reduction of the problem dimension by one) is tarnished to some extent when a fundamental solution to the governing equations does not exist as in the case of nonlinear problems. The easy to implement local point interpolation method applied to the strong form of differential equations is an attractive numerical approach. Its accuracy deteriorates in the presence of Neumann-type boundary conditions which are practically inevitable in solid mechanics. The main appeal of the BEM can be maintained by a judicious coupling of the pure BEM with the local point interpolation method. The resulting approach, named the LPI-BEM, seems versatile and effective. This is demonstrated by considering some linear and nonlinear elasticity problems including multi-physics and multi-field problems.

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