Y.C. Shiah¹, C.L. Tan², Y.H. Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 243-257, 2013, DOI:10.3970/cmes.2013.096.243

Abstract The present authors have recently proposed an efficient, alternative approach to numerically evaluate the fundamental solution and its derivatives for 3D general anisotropic elasticity. It is based on a double Fourier series representation of the exact, explicit form of the Green’s function derived by Ting and Lee (1997). This paper reports on the successful implementation of the fundamental solution and its derivatives based on this Fourier series scheme in the boundary element method (BEM) for 3D general anisotropic elastostatics. Some numerical examples of stress concentration problems and a crack problem are presented to demonstrate the More >

Mikael A. Langthjem¹, Masami Nakano²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 227-241, 2013, DOI:10.3970/cmes.2013.096.227

Abstract This paper is concerned with a mathematical model of a simple axisymmetric silencer-like model, consisting of a hole-tone feedback system equipped with a tailpipe. The unstable shear layer is modeled via a discrete vortex method, based on axisymmetric vortex rings. The aeroacoustic model is based on the Powell- Howe theory of vortex sound. Boundary integrals are discretized via the boundary element method; but the tailpipe is represented by the exact (one-dimensional) solution. It is demonstrated though numerical examples that this numerical model can display lock-in of the self-sustained flow oscillations to the resonant acoustic oscillations. More >

P.H. Wen¹, X.J. Huang¹, M.H. Aliabadi²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.3, pp. 199-225, 2013, DOI:10.3970/cmes.2013.096.199

Abstract In this paper, a Local Integral Equation Method (LIEM) is presented for solving two-dimensional nonlocal elasticity problems . The approach is based on the Eringen’s model with LIEM and the interpolation using the radial basis functions to obtain the numerical solutions for 2D problems. A weak form for the set of governing equations with a unit test function is transformed into the local integral equations. The meshless approximation technique with radial basis functions is employed for the implementation of displacements. A set of the local domain integrals is obtained in analytical form for the local More >

F.C. de Araújo^1,2, C. R. da Silva Jr.¹, M. J. Hillesheim¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.3, pp. 185-198, 2013, DOI:10.3970/cmes.2013.096.185

Abstract In this paper, the BE SBS (subregion-by-subregion) algorithm, a generic substructuring technique for the BEM, is applied to evaluate stresses at boundary and interfacial points of general 3D composites and solids. At inner points, regular boundary integration schemes may be employed. For boundary or interfacial points, the Hooke’s law along with global-to-local axis-rotation transformations is directly applied. In fact, in thin-walled domain parts, only boundary stresses are needed. As the SBS algorithm allows the consideration of a generic number of subregions, the technique applies to the stress analysis in any composite and solid, including the More >

E.A. Chadwick¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.3, pp. 177-184, 2013, DOI:10.3970/cmes.2013.096.177

Abstract In boundary integral methods for Stokes flow, the far-field Green’s integral is usually taken to be zero without proof. However, this is not obviously the case, the reason being that Stokes flow is a near-field approximation and breaks down in the far-field. Here, we show that it is zero as expected by matching it to a far-field Green’s integral in Oseen flow. Hence, there are similarities to the matched asymptotic procedure matching a near-field Stokes flow to a far-field Oseen flow, except in this case a different and new procedure is required to deal with More >

A. Sellier

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.3, pp. 159-176, 2013, DOI:10.3970/cmes.2013.096.159

Abstract The rigid-body migration of a slip and arbitrary-shaped solid particle freely suspended in a prescribed and arbitrary ambient Stokes flow is determined after calculating the hydrodynamic force and torque exerted on the particle when it either experiences a given rigid-body in a quiescent liquid or is held fixed in the ambient Stokes flow. It is also shown how one can subsequently obtain the velocity and surface traction on the particle boundary and thereafter, if necessary, the flow about the particle in the entire liquid domain. The advocated procedure extends a recent work (see Sellier (2012)) More >

L. Rodríguez-Tembleque¹, A. Sáez¹, F.C. Buroni¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.2, pp. 131-158, 2013, DOI:10.3970/cmes.2013.096.131

Abstract A boundary element based formulation is applied to study numerically the tribological behavior of fiber-reinforced plastics (FRP) under different frictional contact conditions, taking into account the micromechanics of FRP. Micromechanical models presented consider continuous and short fiber reinforced plastics configurations. The Boundary Element Method (BEM) with an explicit approach for fundamental solutions evaluation is considered for computing the elastic influence coefficients. Signorini’s contact conditions and an orthotropic law of friction on the potential contact zone are enforced by contact operators over the augmented Lagrangian. The proposed methodology is applied to study carbon FRP under frictional More >

W.L.A. Pereira¹, V.J. Karam², J.A.M. Carrer³, C.S.G. Monteiro¹, W.J. Mansur¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.2, pp. 117-130, 2013, DOI:10.3970/cmes.2013.096.117

Abstract In this work, the BEM is applied to obtain the numerical solutions for free vibration analysis of thick square plates with two edges simply supported or clamped, and the other two edges free. A formulation based on Reissner’s theory is used here, which includes the contribution of the additional translational inertia terms to the integral equation of displacements and internal forces. The boundary element method is used to discretize the space, where it is employed the static fundamental solution. In literature, the responses for the kind of problem addressed here are very important in the More >

A. F. Galvis¹, R. Q. Rodriguez¹, P. Sollero¹, E. L. Alburquerque²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.2, pp. 103-115, 2013, DOI:10.3970/cmes.2013.096.103

Abstract Polycrystalline structures are present on metal alloys. Therefore, it is necessary to understand and model the mechanical behavior of this media. Usually, this is accomplished by the use of different numerical methods. However, the analysis of polycrystalline materials leads to other type of problems, such as high computational requirements generated in order to get an efficient solution. In this work, the 2D polycrystalline structure is generated using an average grain size through the Voronoi tessellation method and discretized through simulations with random material, crystalline orientation and orthotropic behavior [Sfantos and Aliabadi (2007a)]. BEM discretization requires More >

G.R. Baker¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.2, pp. 91-101, 2013, DOI:10.3970/cmes.2013.096.091

Abstract A vortex patch is a bounded region of uniform vorticity in twodimensional, incompressible, inviscid fluid flow. The streamfunction satisfies the Poisson equation with the vorticity acting as a source term. The standard formulation is to write the streamfunction as a convolution of the vorticity with the twodimensional free-space Greens function. A simple application of Greens theorem converts the area integral to a boundary integral. Numerical methods must then account for the singular nature of the boundary integral, and high accuracy is difficult when filamentation takes place, that is, when long, very thin filaments of vorticity… More >