Engineering Transactions, 48, 4, pp. 373–393, 2000

Static and Stability Analysis of Shells with Large Displacements and Finite Rotations

J. Marcinowski
Wroclaw University of Technology

The paper deals with large displacements and finite rotations of elastic shells subjected to the action of external loads. The numerical approach to the problem based on the finite element method in displacement formulation is presented. The degenerated finite element originally introduced by AHMAD et al. [1] and subsequently supplemented by MARCINOWSKI [2] was used in this paper. This very element was essentially suitable for shell problems exhibiting small and moderate rotations, but there exists a possibility to apply it also to problems with finite rotations, provided the updated Lagrangian formulation is adopted. Details of such an approach were presented in the paper. Several examples taken from the literature and confirming the correctness of the applied approach were included.
Full Text: PDF

References

S. AHMAD, B.M. IRONS, O.C. ZIENKIEWICZ, Analysis of thick and thin shell structures by curved finite elements, Int. J. Num. Meth. Engng., 2, 419–451, 1970.

J. MARCINOWSKI, Calculation of nonlinear equilibrium paths of structures [in Polish], Arch, of Civil Engng., XXXV, 3–4, 283–297, 1989.

F. GRUTTMANN, E. STEIN, P. WRIGGERS, Theory and numerics of thin shells with finite rotations, Ingenieur-Archiv, 59, 54–67, 1989.

N. BUECHTER, E. RAMM, Shell theory versus degeneration – a comparison in large rotation finite element analysis, Int. J. Num. Meth. Engng., 34, 39–59, 1992.

J. CHRÓŚCIELEWSKI, J. MAKOWSKI, H. STUMPF, Genuinely resultant shell finite elements accounting for geometric and material nonlinearity, Int. J. Num. Meth. Engng., 35, 63–94, 1992.

C. SANSOUR, H. BUFLER, An exact finite rotation shell theory, its mixed variational for mulation and its finite element implementation, Int. J. Num. Meth. Engng., 34, 73–115, 1992.

K.S. SURANA, Geometrically nonlinear formulation for the curved shell elements, Int. J. Num. Meth. Engng., 19, 581–615, 1983.

S.F. PAWSEY, R.W. CLOUGH, Improved numerical integration of thick shell finite elements, Int. J. Num. Meth. Engng., 3, 575–586, 1971.

O.C. ZIENKIEWICZ, R.L. TAYLOR, J.M. TOO, Reduced integration technique in general analysis of plates and shells, Int. J. Num. Meth. Engng., 3, 275–290, 1971.

K.J. BATHE, E. RAMM, E.L. WILSON, Finite element formulation for large deformation dynamic analysis, Int. J. Num. Meth. Engng., 9, 353–386, 1975.

J.A. STRICKLIN, W.E. HAISLER, Formulations and solution procedures for nonlinear structural analysis, Computers and Structures, 7, 123–136, 1977.

L.E. MALVERN, Introduction to the mechanics of a continuous medium, Prentice–Hall, Inc., Englewood Cliffs, New Jersey 1969.

O.C. ZIENKIEWICZ, Finite element method [in Polish], Arkady, Warszawa 1972.

J. MARCINOWSKI, D. ANTONIAK, Stability of the cylindrical panel. Experimental investigations and numerical analysis, Engng. Trans., 42, 1–2, 61–74, 1994.

J.T. ODEN, Finite elements of nonlinear continua, McGraw–Hill, Inc., 1972.

M. KLEIBER, Finite element method in nonlinear mechanics of solids [in Polish], PWN, Warszawa–Poznań 1985.

R. PRISCH-FAY, A new approach to the analysis of the deflection of thin cantilevers, Proc. ASCE, J. Appl. Mech., 28, 87–90, 1961.

J. MARCINOWSKI, Bifurcation points and branching paths in the nonlinear stability analysis of shell structures, J. Theoret. Appl. Mech., 32, 3, 637–651, 1994.

J.H. ARGYRIS, H. BALMER, J. ST. DOLTSINIS, P.C. DUNNE, M. HAASE, M. KLEIBER, G. MALEJANNAKIS, H.P. MLEJNEK, M. MÜLLER, D.W. SCHARPF, Finite element method – natural approach, Comp. Meth. Appl. Mech. Engng., 17/18, 1–106, 1979.

J.C. SIMO, L. Vu–Quoc, Three-dimensional finite-strain rod model. Part II. Computational aspects, Comp. Meth. Appl. Mech. Engng., 58, 79–116, 1986.

J.C. SIMO, D.D. FOX, M.S. RIFAI, On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory, Comp. Meth. Appl. Mech. Engng., 79, 21–70, 1990.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland