A Novel Boundary Element Method for Linear Elasticity With No Numerical Integration for Two-Dimensional and Line Integrals for Three-Dimensional Problems

1994 ◽  
Vol 61 (2) ◽  
pp. 264-269 ◽  
Author(s):  
A. Nagarajan ◽  
E. Lutz ◽  
S. Mukherjee
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Integration ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Contour Method ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Boundary Contour Method ◽  
Element Method

This paper presents a novel application of the boundary element method to solve problems in linear elasticity. The new method is called the Boundary Contour Method. This approach requires no numerical integration at all for two-dimensional problems and numerical evaluation of line integrals only for three-dimensional problems; even for curved line or surface boundary elements of arbitrary shape! Numerical results are presented for some two-dimensional problems.

The Boundary Contour Method for Three-Dimensional Linear Elasticity

1996 ◽  
Vol 63 (2) ◽  
pp. 278-286 ◽  
Author(s):  
A. Nagarajan ◽  
S. Mukherjee ◽  
E. Lutz
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Contour Method ◽  
Boundary Contour ◽  
Boundary Contour Method ◽  
Novel Variant ◽  
Elasticity Problems ◽  
Element Method

This paper presents a novel variant of the boundary element method, here called the boundary contour method, applied to three-dimensional problems of linear elasticity. In this work, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. Thus, in this formulation, only line integrals have to be numerically evaluated for three-dimensional elasticity problems—even for curved surface elements of arbitrary shape. Numerical results are presented for some three-dimensional problems, and these are compared against analytical solutions.

The Hypersingular Boundary Contour Method for Three-Dimensional Linear Elasticity

1998 ◽  
Vol 65 (2) ◽  
pp. 300-309 ◽  
Author(s):  
S. Mukherjee ◽  
Y. X. Mukherjee
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Boundary Elements ◽  
Contour Method ◽  
Boundary Contour ◽  
Shape Functions ◽  
Boundary Contour Method ◽  
Element Method

A variant of the usual boundary element method, called the boundary contour method, has been presented in the literature in recent years. In the boundary contour method in three-dimensions, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. The boundary contour method employs global shape functions with the weights, in the linear combinations of these shape functions, being defined piecewise on boundary elements. A very useful consequence of this approach is that stresses at points on the boundary of a body, where they are continuous, can be easily obtained from the boundary contour method. The hypersingular boundary element method has many important applications in diverse areas such as wave scattering, fracture mechanics, symmetric Galerkin formulations, and adaptive analysis. This paper first presents the derivation of a regularized hypersingular boundary contour method for three-dimensional linear elasticity. This is followed by a discussion of special cases of the general formulation, as well as some numerical results.

scholarly journals Predicted Absorption Performance of Cylindrical and Rectangular Permeable Membrane Space Sound Absorbers Using the Three-Dimensional Boundary Element Method

2019 ◽  
Vol 11 (9) ◽  
pp. 2714 ◽  
Author(s):  
Masahiro Toyoda ◽  
Kota Funahashi ◽  
Takeshi Okuzono ◽  
Kimihiro Sakagami
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Dimensional Analysis ◽  
Prediction Accuracy ◽  
Sound Absorption ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Permeable Membrane ◽  
Dimensional Boundary ◽  
Element Method

Three-dimensional, permeable membrane space sound absorbers have been proposed as practical and economical alternatives to three-dimensional, microperforated panel space sound absorbers. Previously, the sound absorption characteristics of a three-dimensional, permeable membrane space sound absorber were predicted using the two-dimensional boundary element method, but the prediction accuracy was impractical. Herein, a more accurate prediction method is proposed using the three-dimensional boundary element method. In the three-dimensional analysis, incident waves from the elevation angle direction and reflected waves from the floor are considered, using the mirror image. In addition, the dissipated energy ratio is calculated based on the sound absorption of a surface with a unit sound absorption power. To validate the three-dimensional numerical method, and to estimate the improvement in prediction accuracy, the results are compared with those of the measurements and two-dimensional analysis. For cylindrical and rectangular space sound absorbers, three-dimensional analysis provides a significantly improved prediction accuracy for any shape and membrane sample that is suitable for practical use.

The boundary contour method for three-dimensional linear elasticity with a new quadratic boundary element

1997 ◽  
Vol 20 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Yu Xie Mukherjee ◽  
Subrata Mukherjee ◽  
Xiaolan Shi ◽  
Anantharaman Nagarajan
Keyword(s):  
Boundary Element ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Contour Method ◽  
Boundary Contour ◽  
Boundary Contour Method

Two-Dimensional Green’s Functions for Elastic Bi-materials

1992 ◽  
Vol 59 (2) ◽  
pp. 321-327 ◽  
Author(s):  
J. L. Carvalho ◽  
J. H. Curran
Keyword(s):  
Boundary Element Method ◽  
Hydraulic Fracturing ◽  
Boundary Element ◽  
Plane Strain ◽  
Three Dimensional ◽  
Fundamental Solutions ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Dimensional Plane ◽  
Element Method

Two-dimensional plane-strain fundamental solutions for elastic bi-materials are developed using the nuclei of strain method. The method is a reduction of the threedimensional approach previously derived by Vijayakumar and Cormack. The structure of the three-dimensional solution is preserved and the two-dimensional nuclei of strain and their corresponding vector functions are reported in this paper. Application of these solutions to the boundary element method is demonstrated via a hydraulic fracturing example.

A Review of the Developments in the Boundary Element Method for Time-Domain Elastodynamics

1995 ◽  
Author(s):  
Igor Kaljević ◽  
Sunil Saigal
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Numerical Integration ◽  
Time Domain ◽  
Two Dimensional ◽  
Random Boundary ◽  
Element Method

Abstract The boundary element formulations for two-dimensional time-domain transient elastodynamics are reviewed in this paper. Several improvements of present formulations regarding the numerical integration of boundary element kernels and analysis of symmetric domains are presented. The deterministic transient formulations are next applied for analyzing problems with spatially random boundary conditions. The deficiencies of the present formulations are summarized and possible improvements are suggested.

scholarly journals Application of 3D-FSM Boundary Element Method in Stress and Displacement Analysis of Roadway

2015 ◽  
Vol 9 (1) ◽  
pp. 484-488
Author(s):  
Wang Chong ◽  
Liu Cheng-lun ◽  
Cui Xiaohua
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Integration ◽  
Elastic Body ◽  
Three Dimensional ◽  
Surrounding Rock ◽  
Rational Method ◽  
Displacement Analysis ◽  
Element Method

Conventional fictitious stress methods (FSM) employ numerical integration to calculate displacements or stresses on each element unit. The paper represents a kind of three-dimensional fictitious stress method adopting analytical integrals over triangular leaf elements instead of numerical integration and describes how to analyze stress and displacement of surrounding rock around roadway by the 3D-FSM. The results computed by this method were compared with the results obtained by Flac3d, which proved that it is a correct and rational method to solve three-dimensional mechanics problems especially about hole and crack in an elastic body.

Explicit Kutta condition for unsteady two-dimensional high-order potential boundary element method

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1080-1081
Author(s):  
Giuseppe Davi ◽  
Rosario M. A. Maretta ◽  
Alberto Milazzo
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
High Order ◽  
Two Dimensional ◽  
Kutta Condition ◽  
Element Method
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