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… More >

J. Sorić¹, Q. Li², T. Jarak¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 349-358, 2004, DOI:10.3970/cmes.2004.006.349

Abstract An efficient meshless formulation based on the Local Petrov-Galerkin approach for the analysis of shear deformable thick plates is presented. Using the kinematics of a three-dimensional continuum, the local symmetric weak form of the equilibrium equations over the cylindrical shaped local sub-domain is derived. The linear test function in the plate thickness direction is assumed. Discretization in the in-plane directions is performed by means of the moving least squares approximation. The linear interpolation over the thickness is used for the in-plane displacements, while the hierarchical quadratic interpolation is adopted for the transversal displacement in order More >

H. Okada¹, C. T. Liu², T. Ninomiya¹, Y. Fukui¹, N. Kumazawa¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 333-348, 2004, DOI:10.3970/cmes.2004.006.333

Abstract Formulations and applications of an element overlay technique for the mesoscopic analyses of composite structures are presented in this paper. As a zooming technique, the element overlay technique has been applied to various engineering problems. A finite element mesh having finer mesh discretization is superposed at the region to zoom the spatial resolution of analysis. Such a numerical technique is known as the s-version FEM (S-FEM). This paper aims at developing an S-FEM technique that is suited for the mesoscopic analysis of particulate composite materials. Local finite element models that contain the second phase material… More >

Qing-Sheng Yang^1,2, Wilfried Becker³

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 319-332, 2004, DOI:10.3970/cmes.2004.006.319

Abstract The present paper focuses on the comparative investigation of different homogenization methods for fiber composites, void solids and rigid inclusion media. The effective properties of multi-phase media are calculated by three methods, i.e. direct average method of stress and strain, direct average method of strain energy and two-scale expansion method. A comprehensive comparison, in principle and numerically, of these methods is emphasized. It is obvious that the two direct average methods are identical in principle and therefore they give the same numerical results. It is shown that the two-scale expansion method is the same as More >

J. Sladek¹, V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 309-318, 2004, DOI:10.3970/cmes.2004.006.309

Abstract Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equations which are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry. To eliminate the number of unknowns on artificial boundaries of subdomains the modified fundamental solution and/or the More >

Y. Guo¹, J. A. Nairn¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 295-308, 2004, DOI:10.3970/cmes.2004.006.295

Abstract The Material Point Method (MPM), which is a particle-based, meshless method that discretizes material bodies into a collection of material points (the particles), is a new method for numerical analysis of dynamic solid mechanics problems. Recently, MPM has been generalized to include dynamic stress analysis of structures with explicit cracks. This paper considers evaluation of crack-tip parameters, such as J-integral and stress intensity factors, from MPM calculations involving explicit cracks. Examples for both static and dynamic problems for pure modes I and II or mixed mode loading show that MPM works well for calculation of fracture More >

C.-S. Liu^1,2, C.-W. Chang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 277-294, 2004, DOI:10.3970/cmes.2004.006.277

Abstract This paper delivers several new types of representations of the convex plasticity equation and realizes them by numerical discretizations. In terms of the Gaussian unit vector and the Weingarten map techniques in differential geometry, we prove that the plastic equation exhibits a Lie group symmetry. We convert the nonlinear constitutive equations to a quasilinear equations system X = AX, X ∈ Mⁿ⁺¹, A ∈ so(n,1) in local. In this way the inherent symmetry of the constitutive model of convex plasticity is brought out. The underlying structure is found to be a cone in the Minkowski space Mⁿ⁺¹ More >

Jihan Kim¹, Yong Hyup Kim¹, Sung Won Lee²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 263-276, 2004, DOI:10.3970/cmes.2004.006.263

Abstract The Koiter's asymptotic method is combined with the assumed strain solid shell element formulation for postbuckling analysis of composite and sandwich structures. The assumed strain solid shell element is free of locking and the small angle assumption, and it allows multiple plies through the element thickness. While laminated composite structures are modeled with single element through the thickness, sandwich structures are modeled with three elements stacked through the thickness to model the face sheets and the core independently. The Koiter's method is used to trace initial postbuckling path. Subsequently, the Koiter's method is switched to 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 >

L. G. Zhou¹, L. M. Hsiung², Hanchen Huang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 245-252, 2004, DOI:10.3970/cmes.2004.006.245

Abstract Using molecular dynamics simulations, we study the deformation of polysynthetically twinned (PST) TiAl at room temperature. The simulation cell is pre-strained and thermodynamically relaxed to zero stress, so that no dislocations pre-exist in γ−α₂ interfaces. A uniaxial compression is then applied along one 1/6<112] direction. Our results show that interfacial dislocation pairs nucleate at the γ−α₂ interface under the compression. The glide and agglomeration of these dislocations lead to the nucleation of deformation twins from the interface. Based on our studies, twins may nucleate without pre-existing interfacial dislocations. Further we have monitored the propagation of the More >