Diptiranjan Behera¹, Snehashish Chakraverty²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.5, pp. 317-337, 2013, DOI:10.3970/cmes.2013.096.317

Abstract This paper targets to analyse the static response of structures with fuzzy parameters using fuzzy finite element method. Here the material, geometrical properties and external load applied to the structures are taken as uncertain. Uncertainties presents in the parameters are modelled through convex normalised fuzzy sets. Fuzzy finite element method converts the problem into fuzzy or fully fuzzy system of linear equations for static analysis. As such here, two new methods are proposed to solve the fuzzy and fully fuzzy system of linear equations. Numerical examples for structures with uncertain system parameters that are in term of triangular fuzzy number… More >

L. Godinho¹, D. Dias-da-Costa²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.5, pp. 293-316, 2013, DOI:10.3970/cmes.2013.096.293

Abstract Transient heat conduction problems can be dealt with using different numerical approaches. In some recent papers, a strategy to tackle these problems using a frequency domain formulation has been presented and successfully applied associated to methods such as the BEM. Here a formulation of the meshless local Petrov-Galerkin (MLPG) is developed and presented to allow the analysis of such problems. The proposed formulation makes use of the RBF-based version of the MLPG and employs the Heaviside step function as the test function, leading to the so-called MLPG(5). In addition, the method is associated with a visibility criterion to allow the… More >

B. Pekmen^1,2, M. Tezer-Sezgin^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 275-292, 2013, DOI:10.3970/cmes.2013.096.275

Abstract The dual reciprocity boundary element method (DRBEM) formulation is presented for solving incompressible magnetohydrodynamic (MHD) flow equations. The combination of Navier-Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetics through Ohm’s law is considered in terms of stream function, vorticity and magnetic potential in 2D. The velocity field and the induced magnetic field can be determined through the relations with stream function and magnetic potential, respectively. The numerical results are visualized for several values of Reynolds (Re), Hartmann (Ha) and magnetic Reynolds number (Rem) in a lid-driven cavity, and in a channel with a square cylinder. The well-known characteristics… More >

R. Q. Rodríguez¹, A.F. Galvis¹, P. Sollero¹, E. L. Albuquerque²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 259-274, 2013, DOI:10.3970/cmes.2013.096.259

Abstract Over recent years the rapid evolution of the computational power has motivated the development of new numerical techniques to account for engineering solutions. The Boundary Element Method (BEM) has shown to be a powerful numeric tool for the analysis and solution of many physical and engineering problems. However, BEM fully populated and non-symmetric system matrices implies in higher memory requirements and solution times. This work analyze the application of hierarchical matrices and low rank approximations, applying the Adaptive Cross Approximation - ACA, to multiple inclusion potential problems. The use of hierarchical format is aimed at reducing the storage requirement and… More >

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 veracity of the implementation. 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 elasticity and by using a… 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 microstructural (grain-by-grain) modeling of materials.… 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 the Green’s integrals. In particular,… 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)) and consists in inverting at… More >