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Free-form shell analysis by a mixed-hybrid finite element approach

Berechnung dünnwandiger elastischer Schalen mit Hilfe eines gemischt-hybriden Finite-Element-Verfahrens

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Summary

A novel finite element scheme is proposed for the linear elasto-static analysis of free-form thinwalled shells. On the basis of a modified version of the variational theorem due to Hellinger and Reissner, a doubly curved triangular element is developed with six degrees-of-freedom (three translations plus three rotations) per nodal point. For each element, separate trial functions are introduced in order to approximate the displacements and the stress resultants. It is shown that by properly choosing these interpolants, an element is obtained which (i) is capable of exactly representing the rigid body and constant strain modes; (ii) does not possess any spurious kinematic modes; (iii) fulfils C 1 interelement continuity and (iv) satisfies exactly the interior domain static equilibrium conditions. Two representative examples have been solved in order to illustrate the advantages of the proposed scheme over existing ones.

Übersicht

Die vorliegende Arbeit beschäftigt sich mit der numerischen Berechnung des linearen Trag- und Deformationsverhaltens dünnwandiger Schalentragwerke beliebiger Geometrie. Auf der Grundlage eines modifizierten Funktionals vom Typ Hellinger/Reissner wird ein doppeltgekrümmtes Dreieckselement mit insgesamt achtzehn Freiheitsgraden entwickelt. Im Vergleich mit existierenden Elementen zeichnet sich das hier vorgeschlagene dadurch aus, daß es (i) keine fiktiven Kinematikzustände (‘spurious modes’) besitzt; (ii) in der Lage ist, Starrkörperzustände sowie Zustände konstanter Verzerrungen exakt darzustellen; (iii) einen C 1-stetigen Verschiebungsverlauf an den Zwischenelementrändern garantiert, und (iv) die a-priori-Erfüllung der Gleichgewichtsbedingungen im Elementinneren gewährleistet. Eine Vielzahl von ausgesuchten Testbeispielen sind mit Hilfe des hier vorgestellten Elementeverfahrens gerechnet worden, um sein Konvergenzverhalten sowie seine Zuverlässigeit zu überprüfen. Einige charakteristische Resultate werden im Schlußteil der Arbeit präsentiert.

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References

  1. Adini, A.: Analysis of shell structures by the finite element method. Doctoral Dissertation, University of California, Berkeley 1961

    Google Scholar 

  2. Visser, C.: The approximate analysis of thin shells by the finite element method. Doctoral Dissertation, Ohio State University, Columbus 1966

    Google Scholar 

  3. Utku, S.: Stiffness matrices for the triangular elements of nonzero Gaussian quadrature. AIAA J. 5 (1967) 1659–1667

    Google Scholar 

  4. Clough, R. W.; Johnson, C. Ph.: A finite element approximation for the analysis of thin shells. Int. J. Solids Struct. 4 (1968) 43–60

    Google Scholar 

  5. Fette, H.: Gekrümmte finite Elemente zur Berechnung von Schalentragwerken. Dissertation, TH Braunschweig 1969

    Google Scholar 

  6. Prato, C.: Shell finite element method via Reissner's principle. Int. J. Solids Struct. 5 (1969) 1119–1133

    Google Scholar 

  7. Gallagher, R. H.: The development and evaluation of matrix methods for thin shell structural analysis. Doctoral Dissertation, SUNY Buffalo 1966

    Google Scholar 

  8. Gallagher, R. H.: Shell elements. In: Proc. World Congress on Finite Element Methods in Structural Mechanics, Burnemouth 1975

  9. Timoshenko, S.; Woinowsky-Krieger, S.: Theory of plates and shells. 2nd ed. New York: McGraw Hill 1959

    Google Scholar 

  10. Stein, E.; Berg, A.: Thin elastic shells: theory — funcionals — finite element methods. Seminar notes CISM, Udine 1977

    Google Scholar 

  11. Harbord, R.: Berechnung dünner Schalentragwerke mit finiten Elementen: Vergleichende Untersuchungen unterschiedlicher Diskretisierungsvarianten Bericht KFK-CAD 24, KFK Karlsruhe 1977

  12. Harte, R.: Doppelt gekrümmte finite Dreieckelemente für die lineare und nichtlineare Berechnung allgemeiner Flächentragwerke. Bericht 82-10, Ruhr-Universität Bochum, 1982

  13. Murthy, S. S.; Gallagher, R. H.: A triangular thin-shell finite element based on discrete Kirchhoff theory. Comp. Meth. Appl. Mech. Eng. 54 (1986) 197–222

    Google Scholar 

  14. Stolarski, H.; Belytschko, T.; Carpenter, N.; Kennedy, J. M.: A simple triangular curved shell element for collapse analysis. In: Sobel; Thomas (eds.) Collapse analysis of structures. ASME Publ. PVP- Vol. 84 (1984) 101–102

  15. Argyris, J. H.; Scharpf, D.: The SHEBA family of shell elements for the matrix displacement method. Aeronaut. J. 72 (1968) 873–883

    Google Scholar 

  16. Karamanlidis, D.: A new mixed hybrid finite element model for static and dynamic analysis of thin plates in bending. In: Chen; Lewis (eds.) Recent advances in engineering mechanics and their impact on civil engineering practice. ASCE Publication 1983

  17. Cantin, G.; Clough, R. W.: A curved cylindrical shell finite element. AIAA J. 6 (1968) 1057–1062

    Google Scholar 

  18. Sabir, A. B.; Lock, A. C.: A curved cylindrical shell finite element. Int. J. Mech. Sci. 14 (1972) 125–137

    Google Scholar 

  19. Ashwell, D. G.; Sabir, A. B.: A new cylindrical shell finite element based on simple independent strain function. Int. J. Mech. Sci. 14 (1972) 171–183

    Google Scholar 

  20. Bushnell, D.: Computerized analysis of shells-Governing equations. Comput. Struct. 18 (1984) 471–536

    Google Scholar 

  21. Thomas, G. R.; Gallagher, R. H.: A triangular thin shell finite elementlinear analysis. NASA CR-2482, 1975

  22. Anonymous: ADINA — a finite element program for automatic dynamic incremental non-linear analysis. Rep. AE 81-1, ADINA Eng., Sept. 1981

  23. Bathe, K.-J.; Bolourchi, S.: A geometric and material nonlinear plate and shell element. Comput. Struct. 11 (1980) 23–48

    Google Scholar 

  24. Zienkiewicz, O. C.: The finite element method. 3rd ed. New York: McGraw Hill 1977

    Google Scholar 

  25. Karamanlidis, D.; LeThe, H.: Berechnung dünner Plattentragwerke nach dem Finite-Element-Verfahren. VDI-Forschungsheft Nr. 621, 1984

  26. Marguerre, K.: Zur Theorie der gekrümmten Platte großer Formänderung. Proc. 5th Int. Cong. Appl. Mech., 1983

  27. Karamanlidis, D.: MELINA — Multipurpose element language for Incremental nonlinear analysis (user's manual). Internal Report, Civil Eng. Dept., University of Rhode Island, 1983

  28. Bathe, K.-J.; Dvorkin, E.; Ho, L. W.: Our discrete Kirchhoff and isoparametric shell elements for nonlinear analysis an assessment. Comput. Struct. 16 (1983) 89–98

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, University of Rhode Island, 02881, Kingston, RI, USA

    D. Karamanlidis (Ass. Professor) & R. Jasti (Graduate Student)

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  1. D. Karamanlidis
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  2. R. Jasti
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Karamanlidis, D., Jasti, R. Free-form shell analysis by a mixed-hybrid finite element approach. Ing. arch 57, 459–466 (1987). https://doi.org/10.1007/BF00534547

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