Abstract
In solid mechanics Lagrangian motion descriptions are normally applied where a given reference volume is associated with the same set of material particles at all stages of deformation. Two forms of the Lagrangian description, the total Lagrangian description (TLD) and the updated Lagrangian description (ULD). are noted in the literature see for example [1–5].
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References
BATHE, K-J., RAMM, E. and WILSON, E.L.: Finite element formulations for large deformation dynamic analysis, International Journal of Numerical Methods in Engineering, 9, (1975), pp. 353–386.
CESCOTTO,S., FREY, F. and FONDER, G.: Total and updated Lagrangian descriptions in nonlinear structural analysis: A unified approach, in: Glowinski , R., Rodin, E.Y. and Zienkiewicz, O.C., eds ., Energy Methods in Finite Element Analysis (Wiley, Chichester, 1979), pp. 283–296.
GADALA, M.S.,DOKAINISH, M.A. and ORAVAS, G.AE.: Formulation methods of geometric and material nonlinearity problems, International Journal of Numerical Methods in Engineering, 20, (1984), pp. 887–914.
BATHE, K-J.: Finite element procedures in engineering analysis (Prentice-Hall, Englewood Cliffs, New Jersey, 1982).
MATTIASSON, K. and SAMUELSSON, A.: Total and updated Lagrangian forms of the co-rotational finite element formulation in geometrically and materially nonlinear analysis, in: Numerical Methods for Non-linear Problems, Taylor, C., Hinton, D. and Owen, D.R.J., eds., (Pineridge Press, Swansea, 1984).
MALVERN, L.E.: I ntroductions to the mechanics of a continuous medium, (Prentice-Hall, Englewood Cliffs, New Jersey, 1969).
TRUESDELL, C.: The elements of continuum mechanics (Springer-Verlag, New York, 1965).
PETERSON, A. and PETERSSON, H.: On finite element analysis of geometrically nonlinear problems, Computer Methods in Applied Mechanics and Engineering, 51, (1985), pp. 277–286.
PETERSON, A.: Finite element analysis of structures at high temperatures, Dr. thesis, Publication TVSM-1001, Lund University, Division of Structural Mechanics, Lund, (1984).
ARGYRIS, J.H., BALMER, H., DOLTSINIS, J.St., DUNNE, P.C., HAASE, M., KLEIBER, M., MALEJANNAKIS, G.A., MLEJNEK, H-P., MÜLLER, M. and SCHARPF, D.W.: Finite element method -the natural approach, Computer Methods in Applied Mechanics and Engineering, 17/18, (1979), pp. 1–106.
BELYTSCHKO, T. and HSIEH, B.J.: Nonlinear transient finite element analysis with convected coordinates, International Journal of Numerical Methods in Engineering, 7, (1973), pp. 255–271.
SZILARD, R. : Theory and analysis of plates (Prentice-Hall, Englewood Cliffs, New Jersey, 1974).
DAHLBLOM, O. and PETERSON, A.: CAMFEM -Computer Aided Modelling based on the Finite Element Method, Publication TVSM-3001, Lund University, Division of Structural Mechanics, Lund, (1983).
MATTIASSON, K. : Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals, International Journal of Numerical Methods in Engineering, 17, (1981), pp. 145–153.
LEICESTER, R.H.: Finite deformations of shallow shells, ASCE, Journal of the Engineering Mechanics Division, EM6 , (1968), pp. 1409–1421.
HARTE, R. and ECKSTEIN, U.: Derivation of geometrically nonlinear finite shell elements via tensor notation, International Journal of Numerical Methods in Engineering, 23, (1986), pp. 367–384.
THOMAS, G.R. and GALLAGHER, R.H.: A triangular thin shell finite element: nonlinear analysis, NASA CR-2483, (1975).
HORRIGMOE, G.: Finite element instability analysis of free form shells, Publication No. 77-2, The Norwegian Institute of Technology, Division of Structural Mechanics, The University of Trondheim, Norway, (1977).
BERGAN, P.G. and NYGÅRD, M.K.: Nonlinear shell analysis using free formulation finite elements, Europe-US Symposium Proceedings, (Trondheim, 1985)
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Jingyu, S., Peterson, A., Petersson, H. (1987). Large Displacement Analysis of Thin Shells. In: De Roeck, G., Quiroga, A.S., Van Laethem, M., Backx, E. (eds) Shell and Spatial Structures: Computational Aspects. Lecture Notes in Engineering, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83015-0_31
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DOI: https://doi.org/10.1007/978-3-642-83015-0_31
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