Y.C. Shiah¹, C.L. Tan^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.6, pp. 425-447, 2014, DOI:10.3970/cmes.2014.102.425

Abstract Green’s functions, or fundamental solutions, are necessary items in the formulation of the boundary integral equation (BIE), the analytical basis of the boundary element method (BEM). In the formulation of the BEM for 3D general anisotropic elasticity, considerable attention has been devoted to developing efficient algorithms for computing these quantities over the years. The mathematical complexity of this Green’s function has also posed an obstacle in the development of this numerical method to treat problems of 3D anisotropic thermoelasticity. This is because thermal effects manifest themselves as an additional domain integral in the integral equation;… More >

S. Hamada¹

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 407-424, 2014, DOI:10.3970/cmes.2014.102.407

Abstract The voxel-based indirect boundary element method (IBEM) combined with the Laplace-kernel fast multipole method (FMM) is capable of analyzing relatively large-scale problems. A typical application of the IBEM is the electric field analysis in virtual-human models such as the model called Duke provided by the foundation for research on information technologies in society (IT’IS Foundation). An important property of voxel-version Duke models is that they have various voxel sizes but the same structural feature. This property is useful for examining the O(N) and O(D²) dependencies of the calculation times and the amount of memory required by More >

A. Sellier¹, S. H. Aydin², M. Tezer-Sezgin³

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 393-406, 2014, DOI:10.3970/cmes.2014.102.393

Abstract The fundamental free-space 2D steady creeping MHD flow produced by a concentrated point force of strength g located at a so-called source point x₀ in an unbounded conducting Newtonian liquid with uniform viscosity µ and conductivity σ > 0 subject to a prescribed uniform ambient magnetic field B = Be₁ is analytically obtained. More precisely, not only the produced flow pressure p and velocity u but also the resulting stress tensor field σ are expressed at any observation point x ≠ x₀ in terms of usual modified Bessel functions, the vectors g, x-x₀ and the so-called Hartmann layer thickness d = (√µ/σ)/B More >

Vincenzo Mallardo¹, Eugenio Ruocco²

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 373-391, 2014, DOI:10.3970/cmes.2014.102.373

Abstract The NURBS based isogeometric analysis offers a novel integration between the CAD and the numerical structural analysis codes due to its superior capacity to describe accurately any complex geometry. Since it was proposed in 2005, the approach has attracted rapidly growing research interests and wide applications in the Finite Element context. Only recently, in 2012, it was successfully tested together with the Boundary Element Method. The combination of the isogeometric approach and the Boundary Element Method is efficient since both the NURBS geometrical representation and the Boundary Element Method deal with quantities entirely on the More >

R. Q. Rodríguez^1,2, C. L. Tan², P. Sollero¹, E. L. Albuquerque³

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 359-372, 2014, DOI:10.3970/cmes.2014.102.359

Abstract The efficient evaluation of the fundamental solution for 3D general anisotropic elasticity is a subject of great interest in the BEM community due to its mathematical complexity. Recently, Tan, Shiah, andWang (2013) have represented the algebraically explicit form of it developed by Ting and Lee (Ting and Lee, 1997; Lee, 2003) by a computational efficient double Fourier series. The Fourier coefficients are numerically evaluated only once for a specific material and are independent of the number of field points in the BEM analysis. This work deals with the application of hierarchical matrices and low rank More >

Jean-Philippe Jehl¹, Richard Kouitat Njiwa²

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 345-358, 2014, DOI:10.3970/cmes.2014.102.345

Abstract Extended continuum mechanical approaches are now becoming increasingly popular for modeling various types of microstructured materials such as foams and porous solids. The potential advantages of the microcontinuum approach are currently being investigated in the field of biomechanical modeling. In this field, conducting a numerical investigation of the material response is evidently of paramount importance. This study sought to investigate the potential of the (constrained) microstretch modeling method. The problem’s field equations have been solved by applying a numerical approach combining the conventional isotropic boundary elements method with local radial point interpolation. Our resulting numerical More >

Edmund Chadwick¹, Apostolis Kapoulas

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 331-343, 2014, DOI:10.3970/cmes.2014.102.331

Abstract Boundary element models in inviscid (Euler) flow dynamics for a manoeuvring body are difficult to formulate even for the steady case; Although the potential satisfies the Laplace equation, it has a jump discontinuity in twodimensional flow relating to the point vortex solution (from the 2π jump in the polar angle), and a singular discontinuity region in three-dimensional flow relating to the trailing vortex wake. So, instead models are usually constructed bottom up from distributions of these fundamental solutions giving point vortex thin body methods in two-dimensional flow, and panel methods and vortex lattice methods in three-dimensional… More >

Xiyong Huang¹, M. H. Aliabadi², Z. Sharif Khodaei³

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 291-330, 2014, DOI:10.3970/cmes.2014.102.291

Abstract In this paper, a stochastic dual boundary element formulation is presented for probabilistic analysis of fatigue crack growth. The method involves a direct differentiation approach for calculating boundary and fracture response derivatives with respect to random parameters. Total derivatives method is used to obtain the derivatives of fatigue parameters with respect to random parameters. First- Order Reliability Method (FORM) is applied to evaluate the most probable point (MPP). Opening mode fatigue crack growth problems are used as benchmarks to demonstrate the performance of the proposed method. More >

Akpofure E. Taigbenu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 271-289, 2014, DOI:10.3970/cmes.2014.102.271

Abstract The solutions to inverse heat conduction problems (IHCPs) are provided in this paper by the Green element method (GEM), incorporating the logarithmic fundamental solution of the Laplace operator (Formulation 1) and the timedependent fundamental solution of the diffusion differential operator (Formulation 2). The IHCPs addressed relate to transient problems of the recovery of the temperature, heat flux and heat source in 2-D homogeneous domains. For each formulation, the global coefficient matrix is over-determined and ill-conditioned, requiring a solution strategy that involves the least square method with matrix decomposition by the singular value decomposition (SVD) method, More >

Y.C. Shiah¹, Chung-Lei Hsu¹, Chyanbin Hwu^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 257-270, 2014, DOI:10.3970/cmes.2014.102.257

Abstract As has been well documented for the boundary element method (BEM), a volume integral is present in the integral equation for thermoelastic analysis. Any attempt to directly integrate the integral shall inevitably involve internal discretization that will destroy the BEM’s distinctive notion as a true boundary solution technique. Among the schemes to overcome this difficulty, the exact transformation approach is the most elegant since neither further approximation nor internal treatments are involved. Such transformation for 2D anisotropic thermoelasticity has been achieved by Shiah and Tan (1999) with the aid of domain mapping. This paper revisits More >