A new boundary element method formulation for three dimensional problems in linear elasticity

1987 ◽  
Vol 67 (1-4) ◽  
pp. 107-119 ◽  
Author(s):  
N. Ghosh ◽  
S. Mukherjee
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Method Formulation ◽  
Element Method

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.

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.

scholarly journals A Three-Dimensional Acoustic Boundary Element Method Formulation with Viscous and Thermal Losses Based on Shape Function Derivatives

2018 ◽  
Vol 26 (03) ◽  
pp. 1850039 ◽  
Author(s):  
V. Cutanda Henríquez ◽  
P. Risby Andersen
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Hearing Aids ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Sound Waves ◽  
Acoustic Transducers ◽  
Method Formulation ◽  
Acoustic Boundary Element ◽  
Element Method

Sound waves in fluids are subject to viscous and thermal losses, which are particularly relevant in the so-called viscous and thermal boundary layers at the boundaries, with thicknesses in the micrometer range at audible frequencies. Small devices such as acoustic transducers or hearing aids must then be modeled with numerical methods that include losses. In recent years, versions of both the Finite Element Method (FEM) and the Boundary Element Method (BEM) including viscous and thermal losses have been developed. This paper deals with an improved formulation in three dimensions of the BEM with losses which avoids the calculation of tangential derivatives on the surface by finite differences used in a previous BEM implementation. Instead, the tangential derivatives are obtained from the element shape functions. The improved implementation is demonstrated using an oscillating sphere, where an analytical solution exists, and a condenser microphone as test cases.

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.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

Reduced-Order Modeling of Unsteady Flows About Complex Configurations Using the Boundary Element Method

2002 ◽  
Vol 124 (4) ◽  
pp. 988-993 ◽  
Author(s):  
V. Esfahanian ◽  
M. Behbahani-nejad
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Reduced Order Modeling ◽  
Element Formulation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Naca 0012 ◽  
Element Method

An approach to developing a general technique for constructing reduced-order models of unsteady flows about three-dimensional complex geometries is presented. The boundary element method along with the potential flow is used to analyze unsteady flows over two-dimensional airfoils, three-dimensional wings, and wing-body configurations. Eigenanalysis of unsteady flows over a NACA 0012 airfoil, a three-dimensional wing with the NACA 0012 section and a wing-body configuration is performed in time domain based on the unsteady boundary element formulation. Reduced-order models are constructed with and without the static correction. The numerical results demonstrate the accuracy and efficiency of the present method in reduced-order modeling of unsteady flows over complex configurations.

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