CMES-Vol. 34, No. 3, 2008

Open Access

ARTICLE

Evaluation of Explicit-form Fundamental Solutions for Displacements and Stresses in 3D Anisotropic Elastic Solids
Y. C. Shiah¹, C. L. Tan², V.G. Lee³
CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 205-226, 2008, DOI:10.3970/cmes.2008.034.205
Abstract The main impediment to the development of efficient algorithms for the stress analysis of 3D generally anisotropic elastic solids using the boundary element method (BEM) and the local boundary integral equation (LBIE) meshless method over the years is the complexity of the fundamental solutions and the computational burden to evaluate them. The ability to analytically simplify and reduce them into as explicit a form as possible so that they can be directly computed will offer significant cost savings. In addition, they facilitate easy implementation using existing numerical algorithms with the above-mentioned methods that have been More >

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ARTICLE

A Meshless Method for Nonlinear, Singular and Generalized Sturm-Liouville Problems
S.Yu. Reutskiy¹
CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 227-252, 2008, DOI:10.3970/cmes.2008.034.227
Abstract A new numerical technique for solving generalized Sturm--Liouville problem d²w/dx² + q(x, λ )w = 0, b_l[ λ ,w(a)] = b_r[ λ ,w(b)] = 0 is presented. In is presented. In particular, we consider the problems when the coefficient q(x, λ) or the boundary conditions depend on the spectral parameter λ in an arbitrary nonlinear manner. The method presented is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the eigenvalues. The same technique can be applied to a very wide class of More >

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An Assumed Strain Solid Shell Element Formulation with Transversely Quadratic Displacement
K. Lee¹ and S.W. Lee ²
CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 253-272, 2008, DOI:10.3970/cmes.2008.034.253
Abstract A geometrically nonlinear assumed strain formulation is used to develop a nine-node solid shell element with quadratic displacement through the thickness. The transversely quadratic element allows direct use of the constitutive equations developed for three-dimensional solids, which is convenient when material nonlinearity is involved. The nodal degrees of freedom associated with the quadratic terms in the assumed displacement through the thickness are statically condensed out at the element level. The results of numerical tests conducted on selected example problems demonstrate the validity and effectiveness of the present approach. For the cases involving linear elastic material, More >

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Modeling of Intelligent Material Systems by the MLPG
J. Sladek¹, V. Sladek², P. Solek¹, S.N. Atluri³
CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 273-300, 2008, DOI:10.3970/cmes.2008.034.273
Abstract A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magneto-electric-elastic solids with continuously varying material properties. Stationary and transient dynamic 2-D problems are considered in this paper. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the time-dependence in the governing partial differential equations the Laplace-transform technique is applied to the governing equations, which are satisfied in the Laplace-transformed domain in a weak-form on small subdomains. Nodal points are spread on the analyzed domain, and each More >

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