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 >

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 >

Z. Zhong¹, Y. Dai^1,2, C. C. Mei³, P. Tong^1,4

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 >

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 >

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 >

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 >

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 >

Ori Levin, Wei Shyy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 523-536, 2001, DOI:10.3970/cmes.2001.002.523

Abstract Typical low Reynolds number airfoils suffer from reduced lift-to-drag ratio and are prone to flow separation. In order to improve the aerodynamic performance of such airfoils in an unsteady freestream, the concept of passive control is investigated. In this study, a membrane with varying thickness distribution and mechanical properties is attached on the upper surface of a modified Clark-Y airfoil and is free to move upwards and downwards in response to the pressure difference across it. The response surface method is employed to investigate the individual and collective effects of the membrane's prestress, elastic modulus, and thickness distribution on aerodynamic… More >

S.G. Bardenhagen¹, J.E. Guilkey², K.M. Roessig³, J.U. Brackbill⁴, W.M. Witzel⁵, J.C.Foster⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 509-522, 2001, DOI:10.3970/cmes.2001.002.509

Abstract Contact between deformable bodies is a difficult problem in the analysis of engineering systems. A new approach to contact has been implemented using the Material Point Method for solid mechanics, Bardenhagen, Brackbill, and Sulsky (2000a). Here two improvements to the algorithm are described. The first is to include the normal traction in the contact logic to more appropriately determine the free separation criterion. The second is to provide numerical stability by scaling the contact impulse when computational grid information is suspect, a condition which can be expected to occur occasionally as material bodies move through the computational grid. The modifications… More >

Wen-Hwa Chen¹, Xhu-Ming Guo²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 497-508, 2001, DOI:10.3970/cmes.2001.002.497

Abstract An Element Free Galerkin Method is developed for the analysis of three-dimensional structures. A highly accurate and reliable relation between the number of the quadrature orders n_Q and nodes in a three-dimensional cell n_c, n_Q ≥ ³√n_c + 3, is established to accomplish the required integral calculation in the cell. Based on the theory of topology, the generation of nodes in the solution procedure consists of three sequential steps, say, defining the geometric boundary, arranging inside of the body, and improving numerical accuracy. In addition, by selecting the Dirac Delta function as the weighting function, a three-dimensional scattering sub-domain is… More >