Abstract
The objective of this chapter is to present basic concepts of a consistent and mathematically tractable method of calculating large shape distortions in shells subjected to crash loading. The characteristic feature which distinguishes the present method from all other classical formulations in nonlinear mechanics is that trial deformation functions are postulated on the basis of experimental observations rather then on the basis of expected simplicity of integration schemes. The trial solutions are postulated as global space-time fields rather then local space fields which render solution in one configuration only. Such an approach provides for a natural and convenient means of continuously updating an actual configuration of the shell and therefore, lead to a global rather then incremental formulation of the problem. Another concept is consideration of local deforming regions with floating rather then fixed boundaries with stringent conditions of kinematic continuity at the boundary between neighboring elements. As a result of such a formulation the number of degrees of freedom is dramatically reduced without compromising accuracy of calculations.
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References
J. M. Alexander, An approximate analysis of the collapse of thin cylindrical shells under axial loading, Q J. Mech. Appl. Math., 13, 1, 10–15 (1960).
T. Wierzbicki, W. Abramowicz, The Manual of Crashworthiness Engineering, Volume I — Theoretical Foundation. Volume II — Quasi-Static Progressive Crushing. Volume III — Stability of Progressive Collapse. Volume VII — Dynamic Crush — Methods and Results. Center for Transportation Studies, Massachusetts Institute of Technology, (1987–1991).
W. Abramowicz and T. Wieizbicki, Axial crushing of multi-comer sheet metal columns, J. App. Mech., 56, 1, 113–120 (1989).
T. Wierzbicki and W. Abramowicz, Deep plastic collapse of thin-walled structures, in Structural Failure (T. Wierzbicki and N. Jones Ed.’s), John Wiley, New York (1989).
Abramowicz, W., Jones, N., Dynamic Progressive Buckling of Circular and Square Tubes., Int. J. Impact Engng., 4, 4, 243–270, 1986.
T. Wierzbicki, Concertina tearing of metal plates, Joint MIT-Industry Program on Tanker Safety, Report 12, March 1993.
M. Kleiber and C. Wozniak, Nonlinear Mechanics of Structures, Kluwer Academic Publishers, Dordrecht (1991).
L. E. Malvem, Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, New Jersey (1969).
R. Hill, Extremal paths of plastic work and deformation, J. Mech.Phys. Solids, 34, 5, 511–523 (1986).
H. Petryk, A consistent energy approach to defining stability of plastic defonnation processes, in Stability in the Mechanics of Continua (F. H. Schroeder Ed.), 262–280, Springer-Verlag, Berlin (1981).
W. Abramowicz, Crushing Mechanics of Shell Structures, Institute of Fundamental Technological Research, Polish Academy of Sciences, Report 35 (1981 ) — in polish.
W. Abramowicz, Crush Resistance of ‘T’ ‘Y’ and ‘X’ Sections, Joint MIT-Industry Program on Tanker Safety, Massachusetts Institute of Technology, Report 24 (1994).
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© 1997 Springer Science+Business Media Dordrecht
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Abramowicz, W. (1997). The Macro Element Approach in Crash Calculations. In: Ambrósio, J.A.C., Pereira, M.F.O.S., da Silva, F.P. (eds) Crashworthiness of Transportation Systems: Structural Impact and Occupant Protection. NATO ASI Series, vol 332. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5796-4_13
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DOI: https://doi.org/10.1007/978-94-011-5796-4_13
Publisher Name: Springer, Dordrecht
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