M. Patrício¹, R. Mattheij², G. de With³

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 89-118, 2008, DOI:10.3970/cmes.2008.038.089

Abstract The behaviour of composite materials with periodically distributed constituents is considered. Mathematically, this can be described by a boundary value problem with highly oscillatory coefficient functions. An algorithm is proposed to handle the case when the underlying periodicity is locally disturbed. This procedure is constructed using fundamental concepts from homogenisation theory and domain decomposition techniques. Applications to layered materials are considered. More >

Hsin-Yi Lai¹, C. K. Chen^1,2, Jung-Chang Hsu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.1, pp. 87-116, 2008, DOI:10.3970/cmes.2008.034.087

Abstract An innovative solver for the free vibration of an elastically restrained non-uniform Euler-Bernoulli beam with tip mass of rotatory inertia and eccentricity resting on an elastic foundation and subjected to an axial load is proposed. The technique we have used is based on applying the Adomian modified decomposition method (AMDM) to our vibration problems. By using this method, any$i$th natural frequencies can be obtained one at a time and some numerical results are given to illustrate the influence of the physical parameters on the natural frequencies of the dynamic system. The computed results agree well with those analytical and numerical… More >

Liviu Marin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 99-122, 2008, DOI:10.3970/cmes.2008.030.099

Abstract The application of the method of fundamental solutions (MFS) to inverse boundary value problems associated with the steady-state heat conduction in isotropic media in the presence of sources, i.e. the Poisson equation, is investigated in this paper. Based on the approach of Alves and Chen (2005), these problems are solved in two steps, namely by finding first an approximate particular solution of the Poisson equation and then the numerical solution of the resulting inverse boundary value problem for the Laplace equation. The resulting MFS discretised system of equations is ill-conditioned and hence it is solved by employing the singular value… More >

Sanjay Mittal¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 63-78, 2008, DOI:10.3970/cmes.2008.027.063

Abstract Flow past a circular cylinder looses stability at a Reynolds number,Re~47. It has been shown, in the past, that the linear stability analysis (LSA) of the steady state solution can predict not only the critical Re, but also the non-dimensional frequency, St, of the associated instability. For larger Re the non-linear effects become important and the LSA of the steady-state flow does not predict the correct St. It is shown that, in general, the LSA applied to the time-averaged flow can result in useful information regarding its stability. This idea is applied to the Re = 100 flow past a… More >

Arezoo Emdadi¹, Edward J. Kansa², Nicolas Ali Libre^1,3, Mohammad Rahimian¹, Mohammad Shekarchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.1, pp. 23-42, 2008, DOI:10.3970/cmes.2008.025.023

Abstract We present a new method based upon the paper of Volokh and Vilney (2000) that produces highly accurate and stable solutions to very ill-conditioned multiquadric (MQ) radial basis function (RBF) asymmetric collocation methods for partial differential equations (PDEs). We demonstrate that the modified Volokh-Vilney algorithm that we name the improved truncated singular value decomposition (IT-SVD) produces highly accurate and stable numerical solutions for large values of a constant MQ shape parameter, c, that exceeds the critical value of c based upon Gaussian elimination. More >

Nicolas Ali Libre^1,2, Arezoo Emdadi², Edward J. Kansa^3,4, Mohammad Rahimian², Mohammad Shekarchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.1, pp. 61-80, 2008, DOI:10.3970/cmes.2008.024.061

Abstract The numerical solution of partial differential equations (PDEs) with Neumann boundary conditions (BCs) resulted from strong form collocation scheme are typically much poorer in accuracy compared to those with pure Dirichlet BCs. In this paper, we show numerically that the reason of the reduced accuracy is that Neumann BC requires the approximation of the spatial derivatives at Neumann boundaries which are significantly less accurate than approximation of main function. Therefore, we utilize boundary treatment schemes that based upon increasing the accuracy of spatial derivatives at boundaries. Increased accuracy of the spatial derivative approximation can be achieved by h-refinement reducing the… More >

Z. D. Han, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 41-52, 2007, DOI:10.3970/cmes.2007.021.041

Abstract Straight-forward systematic derivations of the weakly singular boundary integral equations (BIEs) are presented, following the simple and directly-derived approach by Okada, Rajiyah, and Atluri (1989b) and Han and Atluri (2002). A set of weak-forms and their algebraic combinations have been used to avoid the hyper-singularities, by directly applying the "intrinsic properties'' of the fundamental solutions. The systematic decomposition of the kernel functions of BIEs is presented for regularizing the BIEs. The present approach is general, and is applied to developing weakly-singular BIEs for solids and acoustics successfully. More >

R. Vodička¹, V. Mantič², F. París²

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 173-204, 2007, DOI:10.3970/cmes.2007.017.173

Abstract An original approach to solve domain decomposition problems by the symmetric Galerkin boundary element method is developed. The approach, based on a new variational principle for such problems, yields a fully symmetric system of equations. A natural property of the proposed approach is its capability to deal with nonconforming discretizations along straight and curved interfaces, allowing in this way an independent meshing of non-overlapping subdomains to be performed. Weak coupling conditions of equilibrium and compatibility at an interface are obtained from the critical point conditions of the energy functional. Equilibrium is imposed through local traction (Neumann) boundary conditions prescribed on… More >

G. Himpel, E. Kuhl, A. Menzel, P. Steinmann¹

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.2, pp. 119-134, 2005, DOI:10.3970/cmes.2005.008.119

Abstract The changing mass of biomaterials can either be modelled at the constitutive level or at the kinematic level. This contribution attends on the description of growth at the kinematic level. The deformation gradient will be multiplicatively split into a growth part and an elastic part. Hence, in addition to the material and the spatial configuration, we consider an intermediate configuration or grown configuration without any elastic deformations. With such an ansatz at hand, contrary to the modelling of mass changes at the constitutive level, both a change in density and a change in volume can be modelled. The algorithmic realisation… More >

B. Jin^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 253-262, 2004, DOI:10.3970/cmes.2004.006.253

Abstract In this paper, we propose a new numerical scheme for the solution of the Laplace and biharmonic equations subjected to noisy boundary data. The equations are discretized by the method of fundamental solutions. Since the resulting matrix equation is highly ill-conditioned, a regularized solution is obtained using the truncated singular value decomposition, with the regularization parameter given by the L-curve method. Numerical experiments show that the method is stable with respect to the noise in the data, highly accurate and computationally very efficient. More >