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.

scholarly journals Continuum Models of Carbon Nanotube-Based Composites Using the Boundary Element Method

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
Y.J. Liu ◽  
X.L. Chen
Keyword(s):  
Carbon Nanotube ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Integrals ◽  
Matrix Material ◽  
Boundary Integral ◽  
Computational Method ◽  
Cylindrical Shape ◽  
Nearly Singular Integrals ◽  
Element Method

This paper presents some recent advances in the boundary element method (BEM) for the analysis of carbon nanotube (CNT)-based composites. Carbon nanotubes, formed conceptually by rolling thin graphite sheets, have been found to be extremely stiff, strong and resilient, and therefore may be ideal for reinforcing composite materials. However, the thin cylindrical shape of the CNTs presents great challenges to any computational method when these thin shell-like CNTs are embedded in a matrix material. The BEM, based on exactly the same boundary integral equation (BIE) formulation developed by Rizzo some forty years ago, turns out to be an ideal numerical tool for such simulations using continuum mechanics. Modeling issues regarding model selections, representative volume elements, interface conditions and others, will be discussed in this paper. Methods for dealing with nearly-singular integrals which arise in the BEM analysis of thin or layered materials and are crucial for the accuracy of such analyses will be reviewed. Numerical examples using the BEM and compared with the finite element method (FEM) will be presented to demonstrate the efficiency and accuracy of the BEM in analyzing the CNT-reinforced composites.

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.

A State Space Boundary Element Method with Analytical Formulas for Nearly Singular Integrals

2018 ◽  
Vol 31 (4) ◽  
pp. 433-444 ◽  
Author(s):  
Changzheng Cheng ◽  
Dong Pan ◽  
Zhilin Han ◽  
Meng Wu ◽  
Zhongrong Niu
Keyword(s):  
Boundary Element Method ◽  
State Space ◽  
Boundary Element ◽  
Singular Integrals ◽  
Nearly Singular Integrals ◽  
Analytical Formulas ◽  
Space Boundary ◽  
Element Method

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.

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

2020 ◽  
pp. 1475472X2097838
Author(s):  
Bassem Barhoumi ◽  
Jamel Bessrour
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Integrals ◽  
Acoustic Radiation ◽  
Normal Derivative ◽  
Boundary Integral ◽  
Meridian Plane ◽  
Mean Flow ◽  
Transform Method ◽  
Element Method

This paper presents a new numerical analysis approach based on an improved Modal Boundary Element Method (MBEM) formulation for axisymmetric acoustic radiation and propagation problems in a uniform mean flow of arbitrary direction. It is based on the homogeneous Modal Convected Helmholtz Equation (MCHE) and its convected Green’s kernel using a Fourier transform method. In order to simplify the flow terms, a general modal boundary integral solution is formulated explicitly according to two new operators such as the particular and convected kernels. Through the use of modified operators, the improved MBEM approach with flow takes a convective form of the general MBEM approach and has a similar form of the nonflow MBEM formulation. The reference and reduced Helmholtz Integral Equations (HIEs) are implicitly taken into account a new nonreflecting Sommerfeld condition to solve far field axisymmetric regions in a uniform mean flow. For isolating the singular integrations, the modal convected Green’s kernel and its modified normal derivative are performed partly analytically in terms of Laplace coefficients and partly numerically in terms of Fourier coefficients. These coefficients are computed by recursion schemes and Gauss-Legendre quadrature standard formulae. Specifically, standard forms of the free term and its convected angle resulting from the singular integrals can be expressed only in terms of real angles in meridian plane. To demonstrate the application of the improved MBEM formulation, three exterior acoustic case studies are considered. These verification cases are based on new analytic formulations for axisymmetric acoustic sources, such as axisymmetric monopole, axial and radial dipole sources in the presence of an arbitrary uniform mean flow. Directivity plots obtained using the proposed technique are compared with the analytical results.

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.

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