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Boundary Element Formulation (boundary + element_formulation)
Selected AbstractsAn elastodynamic Galerkin Boundary Element Formulation for semi-infinite domains in time-domainPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Lars Kielhorn The present work focuses on the problem of modelling wave propagation phenomena within a 3,d elastodynamic halfspace by use of a symmetric Galerkin Boundary Element formulation. Unfortunately, this formulation requires the evaluation of hypersingular integral kernels which are regularized by integration by parts. In Boundary Element Methods semi,infinite domains are commonly approximated in space by considering just a sufficiently large enough region. Applying this simple discretization to the symmetric formulation implies the evaluation of the hypersingular bilinear form on a truncated mesh which will fail due to the regularization approach. To overcome this drawback a methodology based on infinite elements is presented. The numerical tests show that this approach is promising for treating semi,infinite domains with a symmetric Galerkin scheme. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Boundary element formulation for 3D transversely isotropic cracked bodiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004M. P. Ariza Abstract The boundary traction integral representation is obtained in elasticity when the classical displacement representation is differentiated and combined according to Hooke's law. The use of both traction and displacement integral representations leads to a mixed (or dual) formulation of the BEM where the discretization effort for crack problems is much smaller than in the classical formulation. A boundary element analysis of three-dimensional fracture mechanics problems of transversely isotropic solids based on the mixed formulation is presented in this paper. The hypersingular and strongly singular kernels appearing in the formulation are regularized by using two terms of the displacement series expansion and one term of the traction expansion, at the collocation point. All the remaining integrals are analytically evaluated or transformed by means of Stokes' theorem into regular or weakly singular integrals, which are numerically computed. The method is general and can be used for elements of any shape including quarter-point crack front elements. No change of co-ordinates is required for the integration. The formulation as presented in this paper is something as clear, general and easy to handle as the classical BE formulation. It is used in combination with three-dimensional quadratic and quarter-point elements to obtain accurate results for several different crack problems. Cracks in boundless and finite transversely isotropic domains are studied. The meshes are simple and include only discretization of the crack and the external boundary. The obtained results are in good agreement with those existing in the literature. Copyright © 2004 John Wiley & Sons, Ltd. [source] The radial integration method applied to dynamic problems of anisotropic platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2007E. L. Albuquerque Abstract In this paper, the radial integration method is applied to transform domain integrals into boundary integrals in a boundary element formulation for anisotropic plate bending problems. The inertial term is approximated with the use of radial basis functions, as in the dual reciprocity boundary element method. The transformation of domain integrals into boundary integrals is based on pure mathematical treatments. Numerical results are presented to verify the validity of this method for static and dynamic problems and a comparison with the dual reciprocity boundary element method is carried out. Although the proposed method is more time-consuming, it presents some advantages over the dual reciprocity boundary element method as accuracy and the absence of particular solutions in the formulation. Copyright © 2006 John Wiley & Sons, Ltd. [source] Efficiency of boundary element methods for time-dependent convective heat diffusion at high Peclet numbersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2005M. M. Grigoriev Abstract A higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192: 4281,4298; 4299,4312; 4313,4335) for time-dependent convective heat diffusion in two-dimensions appears to be a very attractive tool for efficient simulations of transient linear flows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. ,t,4,/V2) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and efficiency of BEM formulations for Peclet numbers in the range from 103 to 105. Copyright © 2005 John Wiley & Sons, Ltd. [source] Symmetric Galerkin BEM for multi-connected bodiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2001J. J. Pérez-Gavilán In this paper, it is shown that the symmetric Galerkin boundary element formulation cannot be used in its standard form for multiple connected bodies. This is because the traction integral equation used for boundaries with Neuman boundary condition give non-unique solutions. While this fact is well known from the classical theory of integral equations, the problem has not been fully addressed in the literature related to symmetric Galerkin formulations. In this paper, the problem is reviewed and a general way to deal with it is proposed. The details of the numerical implementation are discussed and an example is solved to demonstrate the effectiveness of the proposed solution. Copyright © 2001 John Wiley & Sons, Ltd. [source] Boundary element analysis of curved cracked panels with adhesively bonded patchesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003P. H. Wen Abstract A new boundary element formulation for analysis of curved cracked panels with adhesively bonded patches is presented in this paper. The effect of the adhesive layer is modelled by distributed body forces (i.e. two in-plane forces, two moments and one out-of-plane force). A coupled boundary integral formulation of a shear deformable plate and two-dimensional plane stress elasticity is used to determine bending and membrane forces along the adhesive layer taking into consideration the compatibility conditions in the patch area. Two numerical examples are presented to demonstrate the efficiency of the proposed method. It is shown that the out-of-plane bending behaviour and panel curvature have significant influence on the magnitude of the stress intensity factors. Copyright © 2003 John Wiley & Sons, Ltd. [source] A BEM-based genetic algorithm for identification of polarization curves in cathodic protection systemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002Panayiotis Miltiadou Abstract The purpose of this work is to apply an inverse boundary element formulation in order to develop efficient algorithms for identification of polarization curves in a cathodic protection system. The problem is to minimize an objective function measuring the difference between observed and BEM-predicted surface potentials. The numerical formulation is based on the application of genetic algorithms, which are robust search techniques emulating the natural process of evolution as a means of progressing towards an optimum solution. Examples of application are included in the paper for different types of polarization curves in finite and infinite electrolytes. The accuracy and efficiency of the numerical results are verified by comparison with standard conjugate gradient techniques. As a result of this research, the genetic algorithm approach is shown to be more robust, independent of the position of the sensors and of initial guesses, and will be further developed for three-dimensional applications. Copyright © 2002 John Wiley & Sons, Ltd. [source] A promising boundary element formulation for three-dimensional viscous flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005Xiao-Wei Gao Abstract In this paper, a new set of boundary-domain integral equations is derived from the continuity and momentum equations for three-dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex-variable technique is used to compute the divergence of velocity for internal points, while the traction-recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||