On the Four-node Quadrilateral Element

authored by

Ulrich Hueck, Peter Wriggers

Abstract

A new formulation for the quadrilateral is presented. The standard bilinear element shape functions are expanded about the element center into a Taylor series in the physical co-ordinates. Then the complete first order terms insure convergence with mesh refinement. Incompatible modes are added to the remaining higher order term, all of these being expanded into a second order Taylor series. The minimization of potential energy yields a constraint equation to eliminate the additional incompatible degrees of freedom on the element level. With the resulting constant and linear gradient operators being uncoupled, the stiffness matrix is written in terms of underintegration and stabilization. Therefore, the new quadrilateral is labeled QS6.

Organisation(s)

Institute of Continuum Mechanics

External Organisation(s)

Siemens AG

Type

Contribution to book/anthology

Pages

47-50

No. of pages

4

Publication date

01.12.2011

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Engineering(all)

Electronic version(s)

https://doi.org/10.1007/978-3-642-17484-1_6 (Access: Unknown)

 

Details in the research portal "Research@Leibniz University"