Gauss-Legendre Numerical Integrations over a Quadrilateral Element in Closed Form

Authors

  • MS Islam Department of Mathematics, University of Dhaka, Dhaka
  • G Saha Department of Mathematics, University of Dhaka, Dhaka
  • N Akter Department of Mathematics, Dhaka City College, Dhaka

DOI:

https://doi.org/10.3329/bjsir.v46i3.9050

Keywords:

Gauss-Legendre quadrature, Numerical integration, Quadrilateral finite element, Stiffness matrix, Closed form

Abstract

In this paper we investigate the stiffness matrix of a general quadrilateral element in closed form using n x n Gauss-Legendre quadrature rule. For this, we propose four types of nodal coordinate transformation. The terms of the matrix are divided into two groups, namely - diagonal and non-diagonal. Only one term (called leading) from each group is computed, and then the remaining fourteen terms are computed from these two leading terms exploited one of the proposed types of coordinate transformation. This leads us a great savings in computational time and memory space. In order to compute the matrix we use these transformations in two ways, and thus two algorithms are given to generate the matrix. Finally, numerical example is given to verify the effectiveness of the present formulation.

Keywords: Gauss-Legendre quadrature; Numerical integration; Quadrilateral finite element; Stiffness matrix; Closed form.

DOI: http://dx.doi.org/10.3329/bjsir.v46i3.9050

BJSIR 2011; 46(3): 399-405

Downloads

Download data is not yet available.
Abstract
98
PDF
291

Downloads

How to Cite

Islam, M., Saha, G., & Akter, N. (2011). Gauss-Legendre Numerical Integrations over a Quadrilateral Element in Closed Form. Bangladesh Journal of Scientific and Industrial Research, 46(3), 399–405. https://doi.org/10.3329/bjsir.v46i3.9050

Issue

Vol. 46 No. 3 (2011)

Section

Articles

License

Bangladesh Council of Scientific and Industrial Research (BCSIR) holds the copyright to all contents published in Bangladesh Journal of Scientific and Industrial Research (BJSIR). A copyright transfer form should be signed by the author(s) and be returned to BJSIR.

The entire contents of the BJSIR are protected under Bangladesh Council of Scientific and Industrial Research (BCSIR) copyrights.

Creative Commons Licence
BJSIR is an open access journal, and articles are distributed under the terms of the Creative Commons Attribution-NonCommercial License (CC BY-NC) Creative Commons Attribution-NonCommercial 4.0 International License which allows others remix, tweak, and build upon the articles non-commercially, and although their new works must also acknowledge and be non-commercial, they don’t have to license their derivative works on the same terms.