Details
| Original language | English |
|---|---|
| Title of host publication | Recent Developments and Innovative Applications in Computational Mechanics |
| Pages | 47-50 |
| Number of pages | 4 |
| Publication status | Published - 1 Dec 2011 |
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.
ASJC Scopus subject areas
- Engineering(all)
- General Engineering
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Recent Developments and Innovative Applications in Computational Mechanics. 2011. p. 47-50.
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
TY - CHAP
T1 - On the Four-node Quadrilateral Element
AU - Hueck, Ulrich
AU - Wriggers, Peter
PY - 2011/12/1
Y1 - 2011/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84889788083&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-17484-1_6
DO - 10.1007/978-3-642-17484-1_6
M3 - Contribution to book/anthology
AN - SCOPUS:84889788083
SN - 9783642174834
SP - 47
EP - 50
BT - Recent Developments and Innovative Applications in Computational Mechanics
ER -