Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-06T05:17:27.444Z Has data issue: false hasContentIssue false
  • English
  • Français

A Modified Gaussian Integration Scheme in Element Free Method

Published online by Cambridge University Press:  05 May 2011

Jopan Sheng ,
Chung-Yue Wang  and
Kuo-Jui Shen
Jopan Sheng*
Affiliation:
Department of Civil Engineering, National Central University, Chungli, Tao-Yuan, Taiwan 32054, R.O.C.
Chung-Yue Wang*
Affiliation:
Department of Civil Engineering, National Central University, Chungli, Tao-Yuan, Taiwan 32054, R.O.C.
Kuo-Jui Shen*
Affiliation:
Department of Civil Engineering, Van Nung Institute of Technology, Chungli, Tao-Yuan, Taiwan 320, R.O.C.
*
*Associate Professor
**Professor
***Lecturer
Get access

Abstract

In this paper, a modified numerical integration scheme is presented that improves the accuracy of the numerical integration of the Galerkin weak form, within the integration cells of the analyzed domain in the element-free methods. A geometrical interpretation of the Gaussian quadrature rule is introduced to map the effective weighting territory of each quadrature point in an integration cell. Then, the conventional quadrature rule is extended to cover the overlapping area between the weighting territory of each quadrature point and the physical domain. This modified numerical integration scheme can lessen the errors due to misalignment between the integration cell and the boundary or interface of the physical domain. Some numerical examples illustrate that this newly proposed integration scheme for element-free methods does effectively improve the accuracy when solving solid mechanics problems.

Keywords

Element-free methodMeshfreeQuadrature ruleWeighting function
Type
Articles
Information
Journal of Mechanics , Volume 18 , Issue 1 , March 2002 , pp. 17 - 27
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Belytschko, T., Lu, Y. Y. and Gu, L., “Element-Free Galerkin Method,” International Journal for Numerical Methods in Engineering, 37, pp. 229–256 (1994).CrossRefGoogle Scholar
2Liu, W., Jun, S. and Zhang, Y., “Reproducing kernel particle methods,” International Journal for Numerical Methods in Fluids, 20, pp. 1081–1106 (1995).CrossRefGoogle Scholar
3Duarte, C. and Oden, J., “Hp Clouds – a Meshless Method to Solve Boundary-Value Problems,” Computer Methods in Applied Mechanics & Engineering, 139, pp. 237–262 (1996).CrossRefGoogle Scholar
4Melenk, J. and Babuska, I., “The Partition of Unity Method: Basic Theory and Applications,” Computer Methods in Applied Mechanics & Engineering, 139, pp. 289–314 (1996).CrossRefGoogle Scholar
5Zhu, T., Zhang, J. and Atluri, S., “A Local Boundary Integral Equation (LBIE) Method in Computational Mechanics and a Meshless Discretization Approach,” Computational Mechanics, 21, pp. 223–235 (1998).CrossRefGoogle Scholar
6Atluri, S and Zhu, T., “A New Meshes Local Petrov-Galerkin (MLPG) Approach in Computational Mechanics,” Computational Mechanics, 22, pp. 117–127 (1998).Google Scholar
7Zhu, T., “A New Meshless Regular Local Boundary Integral Equation (MRLBIE) Approach,” International Journal for Numerical Methods in Engineering, 46, pp. 1237–1252 (1999).3.0.CO;2-O>CrossRefGoogle Scholar
8Sukumar, N., Moran, B. and Belytschko, T., “The Natural Element Method in Solid Mechanics,” International Journal for Numerical Methods in Engineering, 43, pp. 839–887 (1998).3.0.CO;2-R>CrossRefGoogle Scholar
9Chen, G., Ohnishi, Y. and Ito, T., “Development of High-Order Manifold Method,” International Journal for Numerical Methods in Engineering, 43, pp. 685–712 (1998).3.0.CO;2-7>CrossRefGoogle Scholar
10Lancaster, P. and Salkauskas, K., “Surfaces Generated by Moving Least Squares Method,” Mathematics of Computation, 37, pp. 141–158 (1981).CrossRefGoogle Scholar
11Nayroles, B., Touzot, G. and Villon, P., “Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elememts,” Computational Mechanics, 10, pp. 307–318 (1992).CrossRefGoogle Scholar
12Kaljevic, I. and Saigal, S., “An Improved Element Free Galerkin Formulation,” International Journal for Numerical Methods in Engineering, 40, pp. 2953–2974 (1997).3.0.CO;2-S>CrossRefGoogle Scholar
13Belytscho, T., Krongauz, Y., Organ, D. and Fleming, M., “Meshless Methods: an Overview and Recent Developments,” Computer Methods in Applied Mechanics & Engineering, 139, pp. 3–47 (1996).CrossRefGoogle Scholar
14Dolbow, J. and Belytschko, T., “Numerical Integration of the Galerkin Weak Form in Meshfree Methods,” Computational Mechanics, 23, pp. 219–230 (1999).CrossRefGoogle Scholar
15Shi, G.-H., “Manifold Method,” Proceeding of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Berkeley California, U.S.A., pp. 52–204 (1996).Google Scholar
16Gerald, C. F., Applied Numerical Analysis, Addison-Wesley Publishing Company (1978).Google Scholar
17Timoshenko, S. and Goodier, J., Theory of Elasticity, 3rd Edition, McGraw-Hill Book Company (1970).Google Scholar