Open Access
ARTICLE
P. H. Wen1, M. H. Aliabadi1, A. Young2
CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 1-10, 2002, DOI:10.3970/cmes.2002.003.001
Abstract In this paper, applications of the boundary element method to damaged and undamaged aircraft curved panels with mechanical repairs are presented. The effects of fastened repairs are replaced by uniform distribution forces in the area of cross-section of the rivet and can be determined from the compatibility condition of displacements. A coupled boundary integral formulation of a shear deformable plate and two dimensional plane stress elasticity is used to determine the bending and membrane forces on the rivets. Domain integrals in each integral equation are determined using the dual reciprocity method. The stress intensity factors due to bending and membrane… More >
Open Access
ARTICLE
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 meshless methods require background cells.… More >
Open Access
ARTICLE
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 be easily evaluated over regularly… More >
Open Access
ARTICLE
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 are supported by numerical results. More >
Open Access
ARTICLE
Z. Zhong1, Y. Dai1,2, C. C. Mei3, P. Tong1,4
CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 77-86, 2002, DOI:10.3970/cmes.2002.003.077
Abstract In this paper we reexamine the sheet-flow model proposed by Fung and Sobin (1969) for blood flow in capillaries in the pulmonary alveoli from micromechanical point of view. The pulmonary alveolar capillary is assumed to be two parallel membranes connected by periodic tissue posts. Blood is spread out into the very thin layer or sheet between the two membranes. The pulmonary alveolar sheet thus has a microstructure of hexagonal cells. A two-scale theory of homogenization is used to establish the canonical equations for the unit cell. The microscale solution is obtained by means of finite element method and the macroscopic… More >
Open Access
ARTICLE
Olivier Ricou1, Michel Bercovier2
CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 87-102, 2002, DOI:10.3970/cmes.2002.003.087
Abstract In this article, we present a method of reduction of the dimension of the Stokes equations by one in a quasi-cylindrical domain. It takes the special shape of the domain into account by the use of a projection onto a space of polynomials defined over the thickness. The polynomials are defined to fit as well as possible with the variables they approximate. Hence, this method restricted to the first polynomial, recovers the Hele-Shaw approximation.
The convergence of the approximate solution to the continuous one is shown. Under a regularity hypothesis, we
also obtain error estimates.
A description of… More >
Open Access
ARTICLE
E. H. Glaessgen1, W.T. Riddell2, I. S. Raju1
CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 103-116, 2002, DOI:10.3970/cmes.2002.003.103
Abstract The effects of several critical assumptions and parameters on the computation of strain energy release rates for delamination and debond configurations modeled with plate elements have been quantified. The method of calculation is based on the virtual crack closure technique (VCCT), and models of the upper and lower surface of the delamination or debond that use two-dimensional (2D) plate elements rather than three-dimensional (3D) solid elements. The major advantages of the plate element modeling technique are a smaller model size and simpler configurational modeling. Specific issues that are discussed include: constraint of translational degrees of freedom, rotational degrees of freedom… More >
Open Access
ARTICLE
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 work for applications to the… More >
Open Access
ARTICLE
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. Using the moving finite element… More >
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