V. Minutolo¹, E. Ruocco¹, S. Ciaramella¹

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 27-48, 2009, DOI:10.3970/cmes.2009.041.027

Abstract A Field Boundary Element Method (FBEM) for Functionally Graded Materials (FGM) is presented and compared with Isoparametric Finite Element Method. The presented formulation, using the Kelvin's fundamental solution, is able to analyse structures although no fundamental solution is actually known. Isoparametric FGM Finite Element Method is a well established tool for FGM structural analysis. The comparison shows that both FBEM and FEM give accurate results. In the paper, the solution of some examples for 2D plates are reported both using FEM and FBEM. Some comparisons with analytical results are discussed and accuracy of the solutions is highlighted. The comparison between… More >

Marco La Mantia¹, Peter Dabnichki^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.2, pp. 131-154, 2008, DOI:10.3970/cmes.2008.033.131

Abstract A potential flow based boundary element method was devised to obtain the hydrodynamic forces acting on oscillating wings. A new formulation of the unsteady Kutta condition, postulating a finite pressure difference at the trailing edge of the flapping wing and proposed earlier by the authors, is implemented in the numerical procedure. A comparison with published experimental data (Read et al., 2003) is carried out and the three-dimensional computational results showed good agreement, especially if compared with a similar two-dimensional numerical approach (La Mantia and Dabnichki, 2008) and the potential analytical model of Garrick (1936). The need of considering the differences… More >

A.I. Abreu¹, W.J. Mansur¹, D. Soares Jr^1,2, J.A.M. Carrer³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 123-132, 2008, DOI:10.3970/cmes.2008.030.123

Abstract This paper is concerned with the numerical computation of space derivatives of a time-domain (TD-) Boundary Element Method (BEM) formulation for the analysis of scalar wave propagation problems. In the present formulation, the Convolution Quadrature Method (CQM) is adopted, i.e., the basic integral equation of the TD-BEM is numerically substituted by a quadrature formula, whose weights are computed using the Laplace transform of the fundamental solution and a linear multi-step method. In order to numerically compute space derivatives, the present work properly transforms the quadrature weights of the CQM-BEM, adopting the so-called Complex-Variable-Differentiation Method (CVDM). Numerical examples are presented at… More >

E. L. Albuquerque¹, M. H. Aliabadi²

CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.2, pp. 63-74, 2008, DOI:10.3970/cmes.2008.029.063

Abstract This paper presents a boundary element formulation for the analysis of thin shallow shells. Classical plate bending and plane elasticity formulations are coupled and effects of curvature are treated as body forces. The body forces are written as a sum of approximation functions multiplied by coefficients. Domain integrals that arise in the formulation are transformed into boundary integrals by the radial integration method. Two different approximation functions are employed, that is 1 + r and r² log r. The method is applied to several problems and the accuracy of each approximation function is assessed by comparison with results from literature. More >

Chia-Cheng Tsai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 151-162, 2008, DOI:10.3970/cmes.2008.027.151

Abstract In this paper we develop analytical particular solutions for the polyharmonic and the products of Helmholtz-type partial differential operators with Chebyshev polynomials at right-hand side. Our solutions can be written explicitly in terms of either monomial or Chebyshev bases. By using these formulas, we can obtain the approximate particular solution when the right-hand side has been represented by a truncated series of Chebyshev polynomials. These formulas are further implemented to solve inhomogeneous partial differential equations (PDEs) in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). Numerical experiments, which include eighth order PDEs and three-dimensional… More >

S. D. Harris¹, R. Mustata², L. Elliott², D. B. Ingham², D. Lesnic²

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.2, pp. 69-80, 2008, DOI:10.3970/cmes.2008.025.069

Abstract Two homogeneous anisotropic materials are butted together to form a contact surface within a single composite material (the specimen). An inverse boundary element method (BEM) is developed to determine the components of the hydraulic conductivity tensor of each material and the position of the contact surface. A steady state flow is forced through the specimen by the application of a constant pressure differential on its opposite faces. Experimental measurements (simulated) of pressure and average hydraulic flux at exposed boundaries are then used in a modified least squares functional. This functional minimises the gap between the above measured (simulated) values and… More >

D. Soares Jr.¹, M. P. Vinagre²

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.1, pp. 1-8, 2008, DOI:10.3970/cmes.2008.025.001

Abstract This work presents an alternative procedure to compute time-domain electromagnetic fields. The Boundary Element Method is here adopted to numerically analyze wave propagation problems, computing just a so-called primary field (either the electric or the magnetic field can be selected as primary field; the complementary field is here named secondary field). The secondary field is obtained following Maxwell's equations, i.e., considering space derivatives of the primary field (computed by the Complex Variable Method) and time integration procedures. This methodology is more efficient and flexible since fewer systems of equations must be solved at each time-step. At the end of the… More >

F.C. Araújo¹, L.J. Gray²

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.2&3, pp. 103-122, 2008, DOI:10.3970/cmes.2008.024.103

Abstract In recent years, carbon nanotubes (CNTs) have been widely employed to build advanced composites. In this work, a Boundary Element Method (BEM) is applied to 3D representative volume elements (RVEs) to estimate mechanical properties of CNT-based composites. To model the thin-walled nanotubes, special integration procedures for calculating nearly-strongly-singular integrals have been developed. The generic BE substructuring algorithm allows modeling complex CNT-reinforced polymers, containing any number of nanotubes of any shape (straight or curved). The subregion-by-subregion strategy, based on Krylov solvers, makes the independent generation, assembly, and storage of the many parts of the complete BE model possible. Thus, significant memory… More >

Liviu Marin¹, Henry Power¹, Richard W. Bowtell², Clemente Cobos Sanchez², Adib A. Becker¹, Paul Glover²，Arthur Jones¹

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 149-174, 2008, DOI:10.3970/cmes.2008.023.149

Abstract We investigate the reconstruction of a divergence-free surface current distribution from knowledge of the magnetic flux density in a prescribed region of interest in the framework of static electromagnetism. This inverse problem is motivated by the design of gradient coils for use in magnetic resonance imaging (MRI) and is formulated using its corresponding integral representation according to potential theory. A novel boundary element method (BEM) which employs linear interpolation on quadratic surfaces and also satisfies the continuity equation for the current density, i.e. a divergence-free BEM, is presented. Since the discretised BEM system is ill-posed and hence the associated least-squares… More >

R. Criado¹, J.E. Ortiz¹, V. Mantič¹, L.J. Gray^1,2, F. París¹

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.2, pp. 151-164, 2007, DOI:10.3970/cmes.2007.022.151

Abstract A numerical implementation of the Somigliana identity in displacements for the solution of 3D elastic problems in exponentially graded isotropic solids is presented. An expression for the fundamental solution in displacements, U_jl, was deduced by Martin et al. (Proc. R. Soc. Lond. A, 458, pp. 1931--1947, 2002). This expression was recently corrected and implemented in a Galerkin indirect 3D BEM code by Criado et al. (Int. J. Numer. Meth. Engng., 2008). Starting from this expression of U_jl, a new expression for the fundamental solution in tractions T_jl has been deduced in the present work. These quite complex expressions of the… More >