Boundary integral–differential equations and boundary element method for interfacial cracks in three-dimensional piezoelectric media

2004 ◽  
Vol 28 (7) ◽  
pp. 753-762 ◽  
Author(s):  
Ming-Hao Zhao ◽  
Ping-Zhi Fang ◽  
Ya-Peng Shen
Keyword(s):  
Boundary Element Method ◽  
Differential Equations ◽  
Boundary Element ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Piezoelectric Media ◽  
Interfacial Cracks ◽  
Integral Differential Equations ◽  
Element Method

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

Boundary Element Method Analysis of Three-Dimensional Thermoelastic Fracture Problems Using the Energy Domain Integral

2005 ◽  
Vol 73 (6) ◽  
pp. 959-969 ◽  
Author(s):  
R. Balderrama ◽  
A. P. Cisilino ◽  
M. Martinez
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Auxiliary Function ◽  
Boundary Integral ◽  
Crack Advance ◽  
Domain Integral ◽  
Energy Domain ◽  
Element Method

A boundary element method (BEM) implementation of the energy domain integral (EDI) methodology for the numerical analysis of three-dimensional fracture problems considering thermal effects is presented in this paper. The EDI is evaluated from a domain representation naturally compatible with the BEM, since stresses, strains, temperatures, and derivatives of displacements and temperatures at internal points can be evaluated using the appropriate boundary integral equations. Special emphasis is put on the selection of the auxiliary function that represents the virtual crack advance in the domain integral. This is found to be a key feature to obtain reliable results at the intersection of the crack front with free surfaces. Several examples are analyzed to demonstrate the efficiency and accuracy of the implementation.

scholarly journals Development of 3D boundary element method for the simulation of acoustic metamaterials/metasurfaces in mean flow for aerospace applications

2020 ◽  
Vol 19 (6-8) ◽  
pp. 324-346
Author(s):  
Imran Bashir ◽  
Michael Carley
Keyword(s):  
Experimental Data ◽  
Mach Number ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Sound Propagation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Mean Flow ◽  
Low Mach Number ◽  
Element Method

Low-cost airlines have significantly increased air transport, thus an increase in aviation noise. Therefore, predicting aircraft noise is an important component for designing an aircraft to reduce its impact on environmental noise along with the cost of testing and certification. The aim of this work is to develop a three-dimensional Boundary Element Method (BEM), which can predict the sound propagation and scattering over metamaterials and metasurfaces in mean flow. A methodology for the implementation of metamaterials and metasurfaces in BEM as an impedance patch is presented here. A three-dimensional BEM named as BEM3D has been developed to solve the aero-acoustics problems, which incorporates the Fast Multipole Method to solve large scale acoustics problems, Taylor’s transformation to account for uniform and non-uniform mean flow, impedance and non-local boundary conditions for the implementation of metamaterials. To validate BEM3D, the predictions have been benchmarked against the Finite Element Method (FEM) simulations and experimental data. It has been concluded that for no flow case BEM3D gives identical acoustics potential values against benchmarked FEM (COMSOL) predictions. For Mach number of 0.1, the BEM3D and FEM (COMSOL) predictions show small differences. The difference between BEM3D and FEM (COMSOL) predictions increases further for higher Mach number of 0.2 and 0.3. The increase in difference with Mach number is because Taylor’s Transformation gives an approximate solution for the boundary integral equation. Nevertheless, it has been concluded that Taylor’s transformation gives reasonable predictions for low Mach number of up to 0.3. BEM3D predictions have been validated against experimental data on a flat plate and a duct. Very good agreement has been found between the measured data and BEM3D predictions for sound propagation without and with the mean flow at low Mach number.

Three-Dimensional Transient Advective Diffusion by Boundary Element Method using Direct Time Integral of the Fundamental Solution

1990 ◽  
Vol 212 ◽  
Author(s):  
Ryuji Kawamura ◽  
Akira Isono
Keyword(s):  
Boundary Element Method ◽  
Fundamental Solution ◽  
Boundary Element ◽  
Time Integration ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Fluid Analysis ◽  
Chemically Reacting ◽  
Advective Diffusion ◽  
Element Method

ABSTRACTThe advective diffusion analyses have been applied to many fields of science and engineering, such as dispersion for chemically reacting(first-order reaction) substance, thermal transport in fluid, analysis of electromagnetic field caused by a moving magnet. electron transport in semiconductors, underground migration of radioactive waste, and so on. The boundary element method (BEM) has been developed extensively for the last decade to solve these transient advective diffusion equation. The time integrations of the fundamental solution in the boundary integral equation, however, make the BEM application to advective diffusion problems difficult. Therefore, the time integration has been approximated in the past relevant publications. This paper describes the BEM in which the time integration is done analytically, and technique is demonstrated with several examples. Good results have been obtained in the example calculations, where comparisons are made with the results from other numerical codes.

scholarly journals Interlaminar Stresses Analysis of Three-Dimensional Composite Laminates by the Boundary Element Method

2018 ◽  
Vol 34 (6) ◽  
pp. 829-837
Author(s):  
Y. C. Shiah ◽  
M. R. Hematiyan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Composite Laminates ◽  
Singular Integrals ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Interlaminar Stresses ◽  
Composite Layers ◽  
Nearly Singular Integrals ◽  
Element Method

AbstractIn engineering industries, composite laminates have been widely applied for various applications. This work presents an efficient analysis of the interlaminar stresses in three-dimensional thin layered anisotropic composites by the boundary element method (BEM). Due to the nearly singular integrals in the boundary integral equation, the conventional BEM approach cannot be applied to analyze the composite layers that are very thin. The present work employs the self-regularization scheme to analyze the interlaminar stresses in thin anisotropic composites. In the end, a few benchmark examples are presented to show the applicability of the present approach.

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

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

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