Nodal Collocation for the P-Convergent Scheme in Boundary Element Technique

2013 ◽  
Vol 405-408 ◽  
pp. 3139-3142
Author(s):  
Kwang Sung Woo ◽  
Won Seok Jang ◽  
Yoo Mi Kwon ◽  
Jun Hyung Jo
Keyword(s):  
Boundary Element ◽  
Higher Order ◽  
Kernel Functions ◽  
Element Formulation ◽  
Shape Functions ◽  
Collocation Points ◽  
Element Technique ◽  
Scheme Selection ◽  
Shaped Domain ◽  
Hierarchical Pattern

The concept of thep-convergent boundary element modeling has been presented to analyze the potential problem with L-shaped domain. The details of thep-convergent boundary element formulation are discussed. These include the equations of nodal collocation for thep-convergent scheme, selection of higher order hierarchical shape functions, techniques for integrating the product of the kernel functions and corresponding shape functions, strategies for selecting collocation points used in approximating the unknowns associated with the higher order shape functions, and program organizations. A numerical example that demonstrates the performance of thep-convergent boundary element formulation is shown with respect to different arrangement of collocation points including both symmetric non-hierarchical pattern and non-symmetric hierarchical pattern.

Numerical analysis of acoustic radiation properties of laminated composite flat panel in thermal environment: A higher-order finite-boundary element approach

2017 ◽  
Vol 232 (18) ◽  
pp. 3235-3249 ◽  
Author(s):  
Nitin Sharma ◽  
Trupti Ranjan Mahapatra ◽  
Subrata Kumar Panda
Keyword(s):  
Boundary Element ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Acoustic Radiation ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Higher Order ◽  
Element Formulation ◽  
Present Scheme ◽  
Acoustic Responses

In this article, the vibration-induced acoustic responses of laminated composite flat panels subjected to harmonic mechanical excitation under uniform temperature load are investigated numerically. The natural frequencies alongside corresponding modes of the flat panels resting on an infinite rigid baffle are obtained by using finite element method in the framework of the higher-order shear deformation theory. A coupled finite and boundary element formulation is then employed to acquire the acoustic responses. The governing equation for the sound radiaiton from the vibrating structures is derived by solving the Helmholtz wave equation. The vibration and acoustic responses are computed by using the present scheme via an in-house computer code developed in MATLAB environment. In order to avoid any excess thermal loading conditions first, the critical buckling temperature of the panel structure is obtained and authenticated with the benchmark values. Further, the sound power levels for isotropic and laminated composite panels are computed using the present scheme and validated with the existing results in the published literature. Finally, the influence of lamination scheme, support conditions and modular ratio on the acoustic radiation behavior of laminated composite flat panels in an elevated thermal environment is studied through various numerical examples. The thermal load is found to have substantial influence on the stiffness of the panels and the peaks in the free vibration responses tend to shift to lower frequencies for higher temperatures. It is also inferred that the panels radiate less efficiently whereas the overall sound pressure level is found to follow an increasing trend with increasing temperature.

A boundary element formulation using higher order curvilinear edge elements

1998 ◽  
Vol 34 (5) ◽  
pp. 2441-2444 ◽  
Author(s):  
C.J. Huber ◽  
W. Rieger ◽  
M. Haas ◽  
W.M. Rucker
Keyword(s):  
Boundary Element ◽  
Higher Order ◽  
Element Formulation ◽  
Edge Elements

A Higher-Order Poly-Region Boundary Element Method for Steady Thermoviscous Fluid Flows

2004 ◽  
Author(s):  
M. . M. Grigoriev ◽  
G. F. Dargush
Keyword(s):  
Boundary Element ◽  
Boundary Integral Equations ◽  
Fluid Flows ◽  
Boundary Elements ◽  
Higher Order ◽  
Boundary Integral ◽  
Iterative Solvers ◽  
Boundary Element Methods ◽  
Element Formulation ◽  
Thermoviscous Fluid

In this presentation, we re-visit the poly-region boundary element methods (BEM) proposed earlier for the steady Navier-Stokes [1] and Boussinesq [2] flows, and develop a novel higher-order BEM formulation for the thermoviscous fluid flows that involves the definition of the domains of kernel influences due to steady Oseenlets. We introduce region-by-region implementation of the steady-state Oseenlets within the poly-region boundary element fequatramework, and perform integration only over the (parts of) higher-order boundary elements and volume cells that are influenced by the kernels. No integration outside the domains of the kernel influences are needed. Owing to the properties of the convective Oseenlets, the kernel influences are very local and propagate upstream. The localization becomes more prominent as the Reynolds number of the flow increases. This improves the conditioning of the global matrix, which in turn, facilitates an efficient use of the iterative solvers for the sparse matrices [3]. Here, we consider quartic boundary elements and bi-quartic volume cells to ensure a high level resolution in space. Similar to the previous developments [4–6], coefficients of the discrete boundary integral equations are evaluated with the sufficient precision using semi-analytic approach to ensure exceptional accuracy of the boundary element formulation. To demonstrate the attractiveness of the poly-region BEM formulation, we consider a numerical example of the well-known Rayleigh-Benard problem governed by the Boussinesq equations.

scholarly journals Nonlinear mechanics of cracks subjected to indentation

2006 ◽  
Vol 33 (6) ◽  
pp. 766-775 ◽  
Author(s):  
A P Selvadurai
Keyword(s):  
Stress Intensity ◽  
Boundary Element ◽  
Crack Tip ◽  
Elastic Solid ◽  
Friction Stress ◽  
Friction Angle ◽  
Element Formulation ◽  
Plastic Energy ◽  
Crack Problems ◽  
Element Technique

The paper presents the application of a boundary element technique to study the behaviour of plane cracks that are located at corner regions of an elastic solid and open during indentation. In particular, the surfaces of the planes on which indentation takes place also exhibit Coulomb frictional responses and degradation in the friction angle with plastic energy dissipation. An incremental boundary element formulation, in which special singularity elements model the behaviour at the crack tip, is used to examine the crack problems. The methodology is applied to investigate the mode I stress intensity factor at the crack tip located at the base of a V-notch in a test specimen.Key words: indented cracks, boundary element modelling, Coulomb friction, stress intensity factors

A Boundary Element Method for Three-Dimensional Steady Convective Heat Diffusion

2004 ◽  
Author(s):  
M. M. Grigoriev ◽  
G. F. Dargush
Keyword(s):  
Boundary Element ◽  
Convective Heat ◽  
Sparse Matrices ◽  
Three Dimensional ◽  
Higher Order ◽  
Iterative Solvers ◽  
Boundary Element Methods ◽  
Heat Diffusion ◽  
Element Formulation ◽  
Definition Of

Higher-order boundary element methods (BEM) are presented for three-dimensional steady convective heat diffusion at high Peclet numbers. An accurate and efficient boundary element formulation is facilitated by the definition of an influence domain due to convective kernels. This approach essentially localizes the surface integrations only within the domain of influence which becomes more narrowly focused as the Peclet number increases. The outcome of this phenomenon is an increased sparsity and improved conditioning of the global matrix. Therefore, iterative solvers for sparse matrices become a very efficient and robust tool for the corresponding boundary element matrices. In this paper, we consider an example problem with an exact solution and investigate the accuracy and efficiency of the higher-order BEM formulations for high Peclet numbers in the range from 1,000 to 100,000. The bi-quartic boundary elements included in this study are shown to provide very efficient and extremely accurate solutions, even on a single engineering workstation.

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