S.H. Pyo¹, H.K. Lee^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.3, pp. 271-306, 2009, DOI:10.3970/cmes.2009.040.271

Abstract This paper presents a micromechanical approach for predicting the elastic and multi-level damage response of aligned and randomly oriented whisker-/ short fiber-reinforced composites. Based on a combination of Eshelby's micromechanics and the evolutionary imperfect interface approach, the effective elastic moduli of the composites are derived explicitly. The modified Eshelby's tensor for spheroidal inclusions with slightly weakened interface [Qu (1993b)] is extended in the present study to model whiskers or short fibers having mild or severe imperfect interfaces. Aligned and random orientations of spheroidal reinforcements are considered. A multi-level damage model in accordance with the Weibull's probabilistic function is then incorporated… More >

T. Jarak¹, J. Sorić¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 231-262, 2008, DOI:10.3970/cmes.2008.038.231

Abstract A new mixed meshless formulation based on the interpolation of both strains and displacements has been proposed for the analysis of plate deformation responses. Kinematics of a three dimensional solid is adopted and discretization is performed by the nodes located on the upper and lower plate surfaces. The governing equations are derived by employing the local Petrov-Galerkin approach. The approximation of all unknown field variables is carried out by using the same Moving Least Squares functions in the in-plane directions, while linear polynomials are applied in the transversal direction. The shear locking effect is efficiently minimized by interpolating the strain… More >

C. Zheng¹, S. C. Wu^2,3,4, X.H.Tang¹, J. H. Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 149-178, 2008, DOI:10.3970/cmes.2008.038.149

Abstract A novel meshfree poly-cell Galerkin method is developed for problems of elasticity and fracture. To improve accuracy, a poly-cell support is proposed to ensure the alignment of shape function support and the integration domain. By orthonormalizing basis functions, the improved moving least-square is formulated soundly, in which frequent matrix inversions are avoided. The Nitsche's method is introduced to treat the essential boundary conditions. It is found that computed solutions are more accurate than those obtained using the circle support used in standard MLS. Furthermore, numerical results present the superconvergent property, compared with the theoretical values in both displacement and energy… More >

J. Sladek¹, V. Sladek¹, C.L. Tan², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.3, pp. 161-174, 2008, DOI:10.3970/cmes.2008.032.161

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously non-homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdomain to which… More >

Y. H. Liu^1,2, S. S. Chen¹, J. Li¹, Z. Z. Cen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 145-156, 2008, DOI:10.3970/cmes.2008.031.145

Abstract A novel meshless method for structural dynamic analysis is presented and discussed in this paper. It is called meshless local natural neighbour interpolation (MLNNI) method, which uses a meshless spatial approximation based only on nodes. The MLNNI is derived from the generalized meshless local Petrov-Galerkin (MLPG) method as a special case. Local weak forms are developed using weighted residual method locally from the dynamic partial differential equation. In the construction of trial functions, the natural neighbour interpolation (NNI) is employed to simplify the treatment of the essential boundary conditions. The domain integration is evaluated over included Delaunay triangles in each… More >

Dong Ju Woo¹, Jin Oh Yang¹, Beom-Soo Kim¹, Seungsoo Lee¹, Jin Yeon Cho²

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 149-162, 2008, DOI:10.3970/cmes.2008.030.149

Abstract A new orphan-cell-free overset method is proposed to carry out the coupled analysis of overlapping finite element substructures. In the proposed overset method, the meshless MLS (Moving Least Squares) approximation is used to obtain the boundary data for the overlapped interface, whereas the Lagrange interpolation scheme has been commonly used in the conventional overset methods. The meshless character of MLS approximation makes it possible to overcome the problem of orphan-cell, which is often encountered in the conventional overset methods. Further, a new connectivity matrix solution procedure is developed to reduce the computational time in the coupled analysis as a part… More >

J. Sladek¹, V. Sladek¹, P. Solek², P.H. Wen³, S.N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 77-98, 2008, DOI:10.3970/cmes.2008.030.077

Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory is transformed into local integral equations on local subdomains in the base plane of the shell by using a unit test function. Nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which… More >

Shu Li¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 37-56, 2008, DOI:10.3970/cmes.2008.030.037

Abstract In this paper, a method based on a combination of an optimization of directions of orthotropy, along with topology optimization, is applied to continuum orthotropic solids with the objective of minimizing their compliance. The spatial discretization algorithm is the so called Meshless Local Petrov-Galerkin (MLPG) "mixed collocation'' method for the design domain, and the material-orthotropy orientation angles and the nodal volume fractions are used as the design variables in material optimization and topology optimization, respectively. Filtering after each iteration diminishes the checkerboard effect in the topology optimization problem. The example results are provided to illustrate the effects of the orthotropic… More >

M. Haji Mohammadi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.2, pp. 75-94, 2008, DOI:10.3970/cmes.2008.029.075

Abstract In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of steady incompressible flows, governed by the Navier--Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based on only a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction equation (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions respectively over a local subdomain. Radial basis functions (RBF) interpolation is employed in shape function… More >

J. Sladek¹, V. Sladek¹, P. Solek², P.H. Wen³

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.1, pp. 57-76, 2008, DOI:10.3970/cmes.2008.028.057

Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve thermal bending problems described by the Reissner-Mindlin theory. Both stationary and thermal shock loads are analyzed here. Functionally graded material properties with continuous variation in the plate thickness direction are considered here. The Laplace-transformation is used to treat the time dependence of the variables for transient problems. A weak formulation for the set of governing equations in the Reissner-Mindlin theory is transformed into local integral equations on local subdomains in the mean surface of the plate by using a unit test function. Nodal points are randomly spread on the surface… More >