P. H. Wen¹, Y. C. Hon²

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.3, pp. 177-192, 2007, DOI:10.3970/cmes.2007.021.177

Abstract In this paper, we perform a geometrically nonlinear analysis of Reissner-Mindlin plate by using a meshless collocation method. The use of the smooth radial basis functions (RBFs) gives an advantage to evaluate higher order derivatives of the solution at no cost on extra-interpolation. The computational cost is low and requires neither the connectivity of mesh in the domain/boundary nor integrations of fundamental/particular solutions. The coupled nonlinear terms in the equilibrium equations for both the plane stress and plate bending problems are treated as body forces. Two load increment schemes are developed to solve the nonlinear differential equations. Numerical verifications are… More >

L.N. Gergidis, D. Kourounis, S. Mavratzas, A. Charalambopoulos¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 157-176, 2007, DOI:10.3970/cmes.2007.021.157

Abstract A new complete set of scattering eigensolutions of Helmholtz equation in spheroidal geometry is constructed in this paper. It is based on the extension to exterior boundary value problems of the well known Vekua transformation pair, which connects the kernels of Laplace and Helmholtz operators. The derivation of this set is purely analytic. It avoids the implication of the spheroidal wave functions along with their accompanying numerical deficiencies. Using this novel set of eigensolutions, we solve the acoustic scattering problem from a soft acoustic spheroidal scatterer, by expanding the scattered field in terms of it. Two approaches concerning the determination… More >

S.Y. Wang^1,2, K.M. Lim^2,3, B.C. Khoo^2,3, M.Y. Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 1-40, 2007, DOI:10.3970/cmes.2007.021.001

Abstract The level set method is a numerical technique for simulating moving interfaces. In this paper, an unconditionally BIBO (Bounded-Input-Bounded-Output) time-stable consistent meshfree level set method is proposed and applied as a more effective approach to simultaneous shape and topology optimization. In the present level set method, the meshfree infinitely smooth inverse multiquadric Radial Basis Functions (RBFs) are employed to discretize the implicit level set function. A high level of smoothness of the level set function and accuracy of the solution to the Hamilton-Jacobi partial differential equation (PDE) can be achieved. The resulting dynamic system of coupled Ordinary Differential Equations (ODEs)… More >

Kuang-Chong Wu¹, Shyh-Haur Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 147-156, 2007, DOI:10.3970/cmes.2007.020.147

Abstract A formulation for two-dimensional self-similar anisotropic elastodyamics problems is generalized to piezoelectric materials. In the formulation the general solution of the displacements is expressed in terms of the eigenvalues and eigenvectors of a related eight-dimensional eigenvalue problem. The present formulation can be used to derive analytic solutions directly without the need of performing integral transforms as required in Cagniard-de Hoop method. The method is applied to derive explicit dynamic Green's functions. Some analytic results for hexagonal 6mm materials are also derived. Numerical examples for the quartz are illustrated. More >

Ehsan Jabbari¹, Behrouz Gatmiri^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.1, pp. 31-44, 2007, DOI:10.3970/cmes.2007.018.031

Abstract In this paper after a discussion about the evolution of the unsaturated soils' governing differential equations and a brief history of the Green's functions for porous media, the governing equations, i.e., the mathematical model in the presence of heat effects are presented and simplified so as the derivation of the associated Green's functions be in the realm of possibility. The thermal two- and three-dimensional, full- and half-space Green's functions for unsaturated porous media, although in a relatively simplified form, are being introduced for the first time, following the previous works of the authors. The derived Green's functions have been demonstrated… More >

D. Soares Jr.¹, W.J. Mansur^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.2, pp. 153-164, 2005, DOI:10.3970/cmes.2005.008.153

Abstract A coupling procedure is described to perform time-domain numerical analyses of dynamic fluid-structure interaction. The fluid sub-domains, where acoustic waves propagate, are modeled by the Boundary Element Method (BEM), which is quite suitable to deal with linear homogeneous unbounded domain problems. The Finite Element Method (FEM), on the other hand, models the structure sub-domains, adopting a time marching scheme based on implicit Green's functions. The BEM/FEM coupling algorithm here developed is very efficient, eliminating the drawbacks of standard and iterative coupling procedures. Stability and accuracy features are improved by the adoption of different time steps in each sub-domain of the… More >

V.K. Tewary², D.T. Read²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 359-372, 2004, DOI:10.3970/cmes.2004.006.359

Abstract An integrated Green's function and molecular dynamics technique is developed for multiscale modeling of a nanostructure in a semi-infinite crystal lattice. The equilibrium configuration of the atoms inside and around the nanostructure is calculated by using molecular dynamics that accounts for nonlinear interatomic forces. The molecular dynamics is coupled with the lattice statics Green's function for a large crystallite containing a million or more atoms. This gives a fully atomistic description of a nanostructure in a large crystallite that includes the effect of nonlinear forces. The lattice statics Green's function is then related to the anisotropic continuum Green's function that… More >

S. N. Atluri¹, Z. D. Han¹, S. Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 507-518, 2003, DOI:10.3970/cmes.2003.004.507

Abstract The general Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement & traction boundary integral equations are presented, for solids undergoing small deformations. These MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs [given in Han, and Atluri (2003)], which are simply derived by using the gradients of the displacements of the fundamental solutions [Okada, Rajiyah, and Atluri (1989a,b)]. By employing the various types of test functions, in the MLPG-type weak-forms of the non-hyper-singular dBIE and tBIE over the local sub-boundary surfaces, several types of MLPG/BIEs are formulated, while also… More >

António Tadeu, Julieta António¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 477-496, 2001, DOI:10.3970/cmes.2001.002.477

Abstract This paper presents analytical solutions, together with explicit expressions, for the steady state response of homogeneous three-dimensional layered acoustic and elastic formations subjected to a spatially sinusoidal harmonic line load. These formulas are theoretically interesting in themselves and they are also useful as benchmark solutions for numerical applications. In particular, they are very important in formulating three-dimensional elastodynamic problems in layered fluid and solid formations using integral transform methods and/or boundary elements, avoiding the discretization of the solid-fluid interfaces. The proposed Green's functions will allow the solution to be obtained for high frequencies, for which the conventional boundary elements' solution… More >

Yu.A. Melnikov, M.Yu. Melnikov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 291-306, 2001, DOI:10.3970/cmes.2001.002.291

Abstract The use of potential (integral) representations is studied when computing Green's functions for boundary value problems stated for Laplace and biharmonic equations over regions of complex configuration in two dimensions. The emphasis is on the non-traditional potentials, whose observation and source points occupy different sets. Such potentials reduce the original boundary value problems to functional (integral) equations with smooth kernels. Special integral representations are studied, the ones whose kernels are built not of the fundamental solutions of governing differential equations but of the Green's functions for simply shaped regions, which are associated with boundary value problems under consideration. Such integral… More >