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 >

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 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, 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… 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 More >

António Tadeu, Julieta António¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 477-496, 2001, DOI:10.3970/cmes.2001.002.477

Abstract This paper presents analytical solutions, together with explicit expressions, for the steady state response of homogeneous three-dimensional layered acoustic and elastic formations subjected to a spatially sinusoidal harmonic line load. These formulas are theoretically interesting in themselves and they are also useful as benchmark solutions for numerical applications. In particular, they are very important in formulating three-dimensional elastodynamic problems in layered fluid and solid formations using integral transform methods and/or boundary elements, avoiding the discretization of the solid-fluid interfaces. The proposed Green's functions will allow the solution to be obtained for high frequencies, for which 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 >