R. C. Batra¹, H.-K. Ching¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.6, pp. 717-730, 2002, DOI:10.3970/cmes.2002.003.717

Abstract The Meshless Local Petrov-Galerkin (MLPG) method is used to analyze transient deformations near either a crack or a notch tip in a linear elastic plate. The local weak formulation of equations governing elastodynamic deformations is derived. It results in a system of coupled ordinary differential equations which are integrated with respect to time by a Newmark family of methods. Essential boundary conditions are imposed by the penalty method. The accuracy of the MLPG solution is established by comparing computed results for one-dimensional wave propagation in a rod with the analytical solution of the problem. Results… More >

Keejoo Lee¹, Chahngmin Cho², Sung W. Lee¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.3, pp. 339-350, 2002, DOI:10.3970/cmes.2002.003.339

Abstract A geometrically nonlinear assumed strain formulation is introduced in conjunction with bubble function displacements to improve the performance of a nine-node solid shell element. The assumed strain field has been carefully selected to avoid both element locking and undesirable spurious kinematic modes. The results of numerical tests demonstrate that the present approach leads to an element that is significantly less sensitive to mesh distortion than the existing element. More >

Wolfgang Brocks¹, Weidong Qi²

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.3, pp. 313-320, 2002, DOI:10.3970/cmes.2002.003.313

Abstract Results of a numerical study of creep damage development and its effect on the deformation behavior in the Ni-based superalloy IN 738 LC at 850 °C are reported. A continuum damage mechanics based anisotropic damage model has been coupled with the unified model of Chaboche, and is used for the present study. Numerical computations are performed on a plate containing a circular hole under tension. They show that the applied damage model does not cause damage localization and no significant mesh-dependence of the results are observed. More >

T. Nishioka¹, J. Furutuka¹, S. Tchouikov¹, T. Fujimoto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 129-146, 2002, DOI:10.3970/cmes.2002.003.129

Abstract The governing condition of dynamic crack bifurcation phenomena had not been fully elucidated until our recent experimental studies. We found from the experimental results that the energy flux per unit time into a propagating crack tip or into a fracture process zone governs the crack bifurcation. Regarding the numerical simulation of dynamic crack bifurcation, to the authors' knowledge, no accurate simulations have been carried out, due to several unresolved difficulties. In order to overcome the difficulties, for the analysis of dynamic crack bifurcation, we developed a moving finite element method based on Delaunay automatic triangulation. More >

C.C. Tsai¹, D.L. Young², A.H.-D. Cheng³

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 117-128, 2002, DOI:10.3970/cmes.2002.003.117

Abstract This paper describes a combination of the dual reciprocity method (DRM) and the method of fundamental solution (MFS) as a meshless BEM (DRM-MFS) to solve three-dimensional Stokes flow problems by the velocity-vorticity formulation, where the DRM is based on the compactly supported, positive definite radial basis functions (CS-PD-RBF). In the velocity-vorticity formulation, both of the diffusion type vorticity equations and the Poisson type velocity equations are solved by DRM-MFS. Here a typical internal cubic cavity flow and an external flow past a sphere are presented. The results are acceptable. Furthermore, this paper provides a preliminary More >

Weimin Han, Xueping Meng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 65-76, 2002, DOI:10.3970/cmes.2002.003.065

Abstract Interests in meshfree (or meshless) methods have grown rapidly in the recent years in solving boundary value problems arising in mechanics, especially in dealing with difficult problems involving large deformation, moving discontinuities, etc. Rigorous error estimates of a meshfree method, the reproducing kernel particle method, for smooth solutions have been theoretically derived and experimentally tested in Han, Meng (2001). In this paper, we provide an error analysis of the meshfree method for solving problems with singular solutions. The results are presented in the context of one-dimensional problems. The error estimates are of optimal order and More >

Shuyao Long¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 53-64, 2002, DOI:10.3970/cmes.2002.003.053

Abstract Meshless methods have been extensively popularized in literature in recent years, due to their flexibility in solving boundary value problems. The meshless local Petrov-Galerkin(MLPG) method for solving the bending problem of the thin plate is presented and discussed in the present paper. The method uses the moving least-squares approximation to interpolate the solution variables, and employs a local symmetric weak form. The present method is a truly meshless one as it does not need a mesh, either for the purpose of interpolation of the solution or for the integration of the energy. All integrals can More >

Satya N. Atluri¹, Shengping Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 11-52, 2002, DOI:10.3970/cmes.2002.003.011

Abstract A comparison study of the efficiency and accuracy of a variety of meshless trial and test functions is presented in this paper, based on the general concept of the meshless local Petrov-Galerkin (MLPG) method. 5 types of trial functions, and 6 types of test functions are explored. Different test functions result in different MLPG methods, and six such MLPG methods are presented in this paper. In all these six MLPG methods, absolutely no meshes are needed either for the interpolation of the trial and test functions, or for the integration of the weak-form; while other… More >

Y. T. Gu, G. R. Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 463-476, 2001, DOI:10.3970/cmes.2001.002.463

Abstract A meshless method for the analysis of Kirchhoff plates based on the Meshless Local Petrov-Galerkin (MLPG) concept is presented. A MLPG formulation is developed for static and free vibration analyses of thin plates. Local weak form is derived using the weighted residual method in local supported domains from the 4th order partial differential equation of Kirchhoff plates. The integration of the local weak form is performed in a regular-shaped local domain. The Moving Least Squares (MLS) approximation is used to constructed shape functions. The satisfaction of the high continuity requirements is easily met by MLS More >

Xiaozhong Jin¹, Gang Li², N. R. Aluru³

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 447-462, 2001, DOI:10.3970/cmes.2001.002.447

Abstract Meshless methods using least-squares approximations and kernel approximations are based on non-shifted and shifted polynomial basis, respectively. We show that, mathematically, the shifted and non-shifted polynomial basis give rise to identical interpolation functions when the nodal volumes are set to unity in kernel approximations. This result indicates that mathematically the least-squares and kernel approximations are equivalent. However, for large point distributions or for higher-order polynomial basis the numerical errors with a non-shifted approach grow quickly compared to a shifted approach, resulting in violation of consistency conditions. Hence, a shifted polynomial basis is better suited from More >