We explore the use of various element-based reduced quadrature strategies for bivariate and trivariate quadratic and cubic spline elements used in isogeometric analysis. The rules studied encompass tensor-product Gauss and Gauss-Lobatto rules, and certain so-called monomial rules that do no possess a tensor-product structure. The objective of the study is to determine quadrature strategies, which enjoy the same accuracy and stability behavior as full Gauss quadrature, but with significantly fewer quadrature points. Several cases emerge that satisfy this objective and also demonstrate superior efficiency compared with standard b C 0-continuous finite elements of the same order.
|Original language||English (US)|
|Number of pages||45|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Aug 1 2014|
Bibliographical noteFunding Information:
D. Schillinger, S.J. Hossain and T.J.R. Hughes were supported by grants from the Office of Naval Research ( N00014-08-1-0992 ) and the National Science Foundation ( CMMI-01101007 ), with the University of Texas at Austin. D. Schillinger was also supported by the German Research Foundation (Deutsche Forschungsgemeinschaft DFG) under grant SCHI 1249/1-2 . The authors wish to thank C.A. Felippa for his input that motivated the study of Felippa’s rule.
- Gauss-Lobatto integration
- Isogeometric analysis
- Monomial quadrature rules
- Reduced quadrature rules