IMPROVED ENHANCED STRAIN FOUR-NODE ELEMENT WITH TAYLOR EXPANSION OF THE SHAPE FUNCTIONS
1997; Wiley; Volume: 40; Issue: 3 Linguagem: Inglês
10.1002/(sici)1097-0207(19970215)40
ISSN1097-0207
Autores Tópico(s)Aeroelasticity and Vibration Control
ResumoInternational Journal for Numerical Methods in EngineeringVolume 40, Issue 3 p. 407-421 Research Article IMPROVED ENHANCED STRAIN FOUR-NODE ELEMENT WITH TAYLOR EXPANSION OF THE SHAPE FUNCTIONS JOŽE KORELC, JOŽE KORELC Department of Civil Engineering, University of Ljubljana, Jamova 2, Ljubljana, SloveniaSearch for more papers by this authorPETER WRIGGERS, PETER WRIGGERS Institut für Mechanik Technische Hochschule Darmstadt, Hochschulstr. 1 64289 Darmstadt, GermanySearch for more papers by this author JOŽE KORELC, JOŽE KORELC Department of Civil Engineering, University of Ljubljana, Jamova 2, Ljubljana, SloveniaSearch for more papers by this authorPETER WRIGGERS, PETER WRIGGERS Institut für Mechanik Technische Hochschule Darmstadt, Hochschulstr. 1 64289 Darmstadt, GermanySearch for more papers by this author First published: 04 December 1998 https://doi.org/10.1002/(SICI)1097-0207(19970215)40:3 3.0.CO;2-PCitations: 40AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract A class of enhanced strain four-node elements with Taylor expansion of the shape function derivatives is presented. A new concept of enhancement using besides the ‘standard’ enhanced strain fields also two other enhanced fields is developed on the basis of the Hu–Washizu principle. For first-order Taylor expansion enhanced modes become uncoupled, thus only a negligible amount of computing effort for the static condensation of enhanced modes is needed. Furthermore, the formulation permits a symbolic integration, which leads to a closed-form solution for the element tangent matrix. Several numerical examples show that the element is stable, invariant, passes the patch test and yields good results especially in the highly distorted regime. © 1997 by John Wiley & Sons, Ltd. References 1 J. C. Simo and M. S. Rifai, ‘A class of mixed assumed strain methods and the method of incompatible modes’, Int. j. numer. methods eng., 29, 1595–1638 (1990). 10.1002/nme.1620290802 Web of Science®Google Scholar 2 J. C. Simo and F. Armero, ‘Geometrically nonlinear enhanced mixed methods and the method of incompatible modes’, Int. j. numer. methods eng., 33, 1413–1449 (1992). 10.1002/nme.1620330705 Web of Science®Google Scholar 3 U. Andelfinger and E. Ramm, ‘EAS-Elements for Two-dimensions, three-dimensional, plate, shell structures and their equivalence to HR-elements’, Int. j. numer. methods eng., 36, 1311–1337 (1993). 10.1002/nme.1620360805 Web of Science®Google Scholar 4 X. Li, A. J. L. Crook and L. P. R. Lyons, ‘Mixed strain elements for non-linear analysis’, Eng. Comput., 10, 223–242 (1993). 10.1108/eb023904 Google Scholar 5 T. J. R. Hughes, ‘Generalization of selective integration procedure to anisotropic and nonlinear media’, Int. j. numer. methods eng., 15, 1413–1418 (1980). 10.1002/nme.1620150914 Web of Science®Google Scholar 6 W. K. Liu, J. S.-J. Ong and R. A. Uras, ‘Finite element stabilization matrices—a unification approach’, Comput. Methods Appl. Mech. Eng., 53, 13–46 (1985). 10.1016/0045-7825(85)90074-X Web of Science®Google Scholar 7 W. K. Liu, Y. K. Hu and T. Belytschko, ‘Multiple quadrature underintegrated finite elements’, Int. j. numer. methods eng., 37, 3263–3289 (1994). 10.1002/nme.1620371905 Web of Science®Google Scholar 8 U. Hueck and P. Wriggers, ‘A formulation for the four-node quadrilateral element’, Int. j. numer. methods eng., to appear. Google Scholar 9 P. Wriggers and U. Hueck, ‘ A formulation of the QS6-element for large elastic deformations’, Int. j. numer. methods eng., submitted. Google Scholar 10 R. L. Taylor, P. J. Beresford and E. L. Wilson, ‘A non-conforming element for stress analysis’, Int. j. numer. methods eng., 10, 1211–1219 (1976). 10.1002/nme.1620100602 Web of Science®Google Scholar 11 R. Piltner and R. L. Taylor, ‘A quadrilateral mixed finite element with two enhanced strain modes’, Int. j. numer. methods eng., 38, 1783–1808 (1995). 10.1002/nme.1620381102 Web of Science®Google Scholar 12 E. L. Wilson, R. L. Taylor, W. P. Doherty and J. Ghaboussi, ‘ Incompatible displacement models’, in Numerical and Computer Models in Structural Mechanics, Academic Press, New York, 1973. 10.1016/B978-0-12-253250-4.50008-7 Google Scholar 13 J. Korelc, ‘ SMS symbolic mechanics system’, Report No. 1/95, Institut für Mechanik, Technische Hochschule Darmstadt, Darmstadt, Germany (1995). Google Scholar 14 O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Vol. 1, 4th edn, McGraw-Hill, London, 1989. Google Scholar 15 J. C. Simo and T. J. R. Hughes, ‘On the variational foundations of assumed strain methods’, J. Appl. Mech. ASME, 53, 51–54 (1986). 10.1115/1.3171737 Web of Science®Google Scholar 16 T. H. H. Pian and K. Sumihara, ‘Rational approach for assumed stress finite elements’, Int. j. numer. methods eng., 20, 1685–1695 (1984). 10.1002/nme.1620200911 Web of Science®Google Scholar 17 J. C. Simo, F. Armero and R. L. Taylor, ‘Improved version of assumed enhanced strain tri-linear elements for 3D finite deformation problems’, Comput. Methods Appl. Mech. Eng., to appear. Google Scholar 18 K. Y. Sze, ‘Efficient formulation of robust hybrid elements using orthogonal stress/strain interpolations and admissible matrix formulation’, Int. j. numer. methods eng., 35, 1–20 (1992). 10.1002/nme.1620350102 Web of Science®Google Scholar 19 K. Y. Sze, ‘Finite element formulation by parametrized hybrid variational principle: variable stiffness and removal of locking’, Int. j. numer. methods eng., 37, 2797–2818 (1994). 10.1002/nme.1620371607 Web of Science®Google Scholar 20 W. K. Liu, T. Belytschko and J.-S. Chen, ‘Nonlinear version of flexurally superconvergent elements’, Comput. Methods Appl. Mech. Eng., 71, 241–258 (1988). 10.1016/0045-7825(88)90034-5 Web of Science®Google Scholar 21 S. Wolfram, Mathematica: A System for Doing Mathematics by Computer, Addison-Wesley, Reading, MA, 1991. Google Scholar Citing Literature Volume40, Issue315 February 1997Pages 407-421 ReferencesRelatedInformation
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