J. S. Ren^*

Molecular & Cellular Biomechanics, Vol.4, No.1, pp. 55-66, 2007, DOI:10.3970/mcb.2007.004.055

Abstract Formation and rupture of aneurysms due to the inflation of an artery with collagen fibers distributed in two preferred directions, subjected to internal pressure and axial stretch are examined within the framework of nonlinear elasticity. A two layer tube model with a fiber-reinforced composite based incompressible anisotropic hyperelastic constitutive material is employed to model the stress-strain behavior of the artery wall with distributed collagen fibers. The artery wall takes up a uniform inflation deformation, and there are no aneurysms in the artery under the normal condition. But an aneurysm may be formed in arteries when… More >

J.N. Johnson¹, J.M. Owen²

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 165-188, 2007, DOI:10.3970/cmes.2007.022.165

Abstract In this paper, we propose a Meshless Local Petrov-Galerkin method for studying the diffusion of a magnetic field within a non-magnetic (μ = μ₀) conducting medium with non-homogeneous and anisotropic electrical resistivity. We derive a local weak form for the magnetic diffusion equation and discuss the effects of different trial/test functions and nodal spacings on its solution. We then demonstrate that the method produces convergent results for several relevant one-dimensional test problems for which solutions are known. This method has the potential to be combined with other mesh-free methods such as Smoothed Particle Hydrodynamics (SPH) to More >

Ping’en Li¹, Xianyue Su^1,2, Youquan Yin¹

CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 93-102, 2007, DOI:10.3970/cmc.2007.006.093

Abstract Based on the perturbation method, for flexural wave in cased hole in anisotropic formation, the alteration in the phase velocity caused by the differences in elastic constants between anisotropic formation of interest and a reference, or unperturbed isotropic formation is obtained. Assuming the cased hole is well bonded, the Thomson-Haskell transfer matrix method is applied to calculate the dispersion relation of flexural wave in cased hole in unperturbed isotropic formation. Both the cases of a fast and slow formation are considered where the symmetry axis of a transversely isotropic (TI) formation makes an angle with… More >

P.D. Shah¹, Ch. Song², C.L. Tan¹, X. Wang¹

Structural Durability & Health Monitoring, Vol.2, No.4, pp. 225-238, 2006, DOI:10.3970/sdhm.2006.002.225

Abstract Numerical T-stress solutions in two dimensional anisotropic cracked bodies are very scarce in the literature. Schemes to evaluate this fracture parameter in anisotropy have been reported only fairly recently. Among them are those developed in conjunction with two different computational techniques, namely, the Boundary Element Method (BEM) and the Scaled Boundary Finite-Element Method (SBFEM). This paper provides a review of the respective schemes using these techniques and demonstrates their efficacy with three examples. These examples, which are of engineering importance, involve cracks lying in a homogeneous medium as well as at the interface between dissimilar media. More >

Y.C. Shiah¹, Y.C. Lin¹, C. L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 15-26, 2006, DOI:10.3970/cmes.2006.016.015

Abstract In this paper, the order of singularity of the integrals appearing in the boundary integral equation for two-dimensional BEM analysis in anisotropic elasticity is reduced using integration by parts. The integral containing the traction fundamental solution is then analytically integrated to give an exact formulation for a general element of n-order interpolation of the variables. This allows the integrals to be very accurately evaluated even for very thin, slender bodies without the need for excessively refined meshes as in conventional BEM analysis. Three example problems involving thin, layered materials are presented to demonstrate the veracity and More >

B. Yang², V. K. Tewary³

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 165-178, 2006, DOI:10.3970/cmes.2006.015.165

Abstract Green's function (GF) modeling of defects may take effect only if the GF as well as its various integrals over a line, a surface and/or a volume can be efficiently evaluated. The GF is needed in modeling a point defect, while integrals are needed in modeling line, surface and volumetric defects. In a matrix of multilayered, generally anisotropic and linearly elastic and piezoelectric materials, the GF has been derived by applying 2D Fourier transforms and the Stroh formalism. Its use involves another two dimensions of integration in the Fourier inverse transform. A semi-analytical scheme has… More >

P.D. Shah¹, C.L. Tan^1,2, X. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.3, pp. 185-198, 2006, DOI:10.3970/cmes.2006.013.185

Abstract In this paper, the path independent mutual or M-integral for the computation of the T-stress for interface cracks between dissimilar anisotropic, linear elastic solids, is developed. The required auxiliary field solution is derived from the solution of the problem of an anisotropic composite wedge subjected to a point force at its apex. The Boundary Element Method (BEM) is employed for the numerical stress analysis in which special crack-tip elements with the proper oscillatory traction singularity are used. The successful implementation of the procedure for evaluating the T-stress in a bi-material interface crack and its application are demonstrated More >

J. Sladek¹, V. Sladek, Ch.Zhang²

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 131-144, 2005, DOI:10.3970/sdhm.2005.001.131

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-d), anisotropic and linear elastic solids with continuously varying material properties. Both quasi-static and transient elastodynamic problems are considered. For time-dependent problems, the Laplace-transform technique is utilized. A unit step function is used as the test function in the local weak-form. It is leading to local boundary integral equations (LBIEs) involving only a domain-integral in the case of transient dynamic problems. The analyzed domain is divided into small subdomains with a circular shape. The moving least-squares (MLS) method is More >

Y.C. Shiah¹, T.L. Guao¹, C.L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 321-338, 2005, DOI:10.3970/cmes.2005.007.321

Abstract It is well known in elastic stress analysis using the boundary element method (BEM) that an additional volume integral appears in the basic form of the boundary integral equation if thermal effects are considered. In order to restore this general numerical tool as a truly boundary solution technique, it is perhaps most desirable to transform this volume integral exactly into boundary ones. For general 2D anisotropic thermo-elastostatics without heat sources, this was only achieved very recently. The presence of concentrated heat sources in the domain, however, leads to singularities at these points that pose additional More >

J. Sladek¹, V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 477-490, 2004, DOI:10.3970/cmes.2004.006.477

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the LBIEs are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry such as circles in 2-d problems. The final form of local integral equations has a More >