Shunde Yin¹, Leo Rothenburg¹, Maurice B. Dusseault¹

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 111-120, 2007, DOI:10.3970/cmes.2007.019.111

Abstract Subsidence problem is of great importance in petroleum engineering and environmental engineering. In this paper, we firstly apply a hybrid Displacement Discontinuity-FEM modeling to this classic problem: the evaluation of subsidence over a compacting oil reservoir. We use displacement discontinuity method to account for the reservoir surrounding area, and finite element methods in the fully coupled simulation of the reservoir itself. This approach greatly reduces the number of degrees of freedom compared to an analyzing fully coupled problem using only a finite element or finite difference discretization. More >

C. P. Providakis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.3, pp. 247-258, 2007, DOI:10.3970/cmes.2007.018.247

Abstract The method of Domain/Boundary Element is used to achieve a dynamic analysis of elastoplastic thick plates resting on internal supports. All possible boundary conditions on the edge of the plate with any interior support conditions such as isolated points (column), lines (walls) or regions (patches) can be treated without practical difficulties. The formulation presented includes the effects of shear deformation and rotatory inertia following Reissner-Mindlin's deformation theory assumptions. The method employs the elastostatic fundamental solution of the problem resulting in both boundary and domain integrals due to inertia, plasticity and interior support effect terms. By discretizing the integral equations and… More >

A. J. Davies¹, D. Crann¹, S. J. Kane¹, C-H. Lai²

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.2, pp. 79-86, 2007, DOI:10.3970/cmes.2007.018.079

Abstract The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The… More >

Ehsan Jabbari¹, Behrouz Gatmiri^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.1, pp. 31-44, 2007, DOI:10.3970/cmes.2007.018.031

Abstract In this paper after a discussion about the evolution of the unsaturated soils' governing differential equations and a brief history of the Green's functions for porous media, the governing equations, i.e., the mathematical model in the presence of heat effects are presented and simplified so as the derivation of the associated Green's functions be in the realm of possibility. The thermal two- and three-dimensional, full- and half-space Green's functions for unsaturated porous media, although in a relatively simplified form, are being introduced for the first time, following the previous works of the authors. The derived Green's functions have been demonstrated… More >

J.A. Sanz, M. Solis, J. Dominguez¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 215-230, 2007, DOI:10.3970/cmes.2007.017.215

Abstract A general mixed boundary element formulation for three-dimensional piezoelectric fracture mechanics problems is presented in this paper. The numerical procedure is based on the extended displacement and traction integral equations for external and crack boundaries, respectively. Integrals with strongly singular and hypersingular kernels appearing in the formulation are analytically transformed into weakly singular and regular integrals. Quadratic boundary elements and quarter-point boundary elements are implemented in a direct way in a computer code. Electric and stress intensity factors are directly computed from nodal values at quarter-point elements. Crack problems in 3D piezoelectric bounded and unbounded solids are solved. The obtained… More >

G. Dziatkiewicz¹ and P. Fedelinski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 35-46, 2007, DOI:10.3970/cmes.2007.017.035

Abstract The aim of the present work is to show the formulation and application of the dual reciprocity boundary element method (BEM) to free vibrations of two-dimensional piezoelectric structures. The piezoelectric materials are modelled as homogenous, linear -- elastic, transversal isotropic and dielectric. Displacements and electric potentials are treated as generalized displacements and tractions and electric charge flux densities are treated as generalized tractions. The static fundamental solutions, which are required in the proposed approach, are derived using the Stroh formalism. The domain inertial integral is transformed to the equivalent boundary integral using the dual reciprocity method (DRM). The boundary quantities… More >

P. A. C. Porto¹, A. B. Jorge¹, G. O. Ribeiro²

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 65-78, 2005, DOI:10.3970/cmes.2005.010.065

Abstract This work deals with a numerical solution technique for the self-regular gradient form of Green's identity, the flux boundary integral equation (flux-BIE). The required C^1,α inter-element continuity conditions for the potential derivatives are imposed in the boundary element method (BEM) code through a non-symmetric variational formulation. In spite of using Lagrangian C⁰ elements, accurate numerical results were obtained when applied to heat transfer problems with singular or quasi-singular conditions, like boundary points and interior points which may be arbitrarily close to the boundary. The numerical examples proposed show that the developed algorithm based on the self-regular flux-BIE are highly efficient,… More >

Ch. Zhang², A. Savaidis³

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 603-618, 2003, DOI:10.3970/cmes.2003.004.603

Abstract A novel non-hypersingular time-domain traction BEM is presented for three-dimensional (3-D) transient elastodynamic crack analysis. The initial-boundary value problem is formulated as a set of non-hypersingular time-domain traction boundary integral equations (BIEs). To solve the time-domain traction BIEs, a time-stepping scheme based on the convolution quadrature formula of Lubich (1988a,b; 1994) for temporal discretization and a collocation method for spatial discretization is adopted. Numerical examples are given for an unbounded solid with a penny-shaped crack under a tensile and shear impact loading. A comparison of the present time-domain BEM with the conventional one shows that the novel time-domain method is… More >

J. P. Agnantiaris¹, D. Polyzos^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 197-212, 2003, DOI:10.3970/cmes.2003.004.197

Abstract A Boundary Element Method (BEM), for the three-dimensional solution of both non-axisymmetric and axisymmetric coupled acoustic-elastic problems in the frequency domain, is presented. The present BEM makes use of the Burton and Miller integral equation for infinite acoustic spaces, while elastic structures are dealt with the standard boundary integral equation of elastodynamics. The axisymmetric formulation involves the use of the fast Fourier transform algorithm. Highly accurate numerical algorithms are used for the evaluation of singular integrals, while nearly singular integrals are treated, also with high accuracy, through the use of practical numerical techniques, for both the axisymmetric and non-axisymmetric cases.… More >

A. Aimi¹, M. Diligenti¹, F. Lunardini¹, A. Salvadori²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 31-50, 2003, DOI:10.3970/cmes.2003.004.031

Abstract This paper is devoted to the study of a new application of the Panel Clustering Method [Hackbusch and Sauter (1993); Hackbusch and Nowak (1989)]. By considering a classical 3D Neumann screen problem in its boundary integral formulation discretized with the Galerkin BEM, which requires the evaluation of double integrals with hypersingular kernel, we recall and use some recent results of analytical evaluation of the inner hypersingular integrals. Then we apply the Panel Clustering Method (PCM) for the evaluation of the outer integral. For this approach error estimate is shown. Numerical examples and comparisons with classical PCM technique are presented. More >