Summary
A nonlinear shell theory is derived for large strain—large beding deformations of shells composed of highly nonlinear materials. Expressions for the stress resultants and stress couples are presented. The equilibrium equations are obtained as weak solution of the stationary principle of total potential energy. A modified Kirchhoff hypothesis is used which accounts for thickness changes as well as for a shift in the location of the original midsurface of the shell. As example the eversion of a spherical shell is calculated numerically.
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Schmidt, R.: Mechanics of materials and structural theories. A current trend in shell theory: Constrained geometrically nonlinear Kirchhoff-Love type theories based on polar decomposition of strains and rotations. Comp. Struct.20, (1–3), 265–275 (1985).
Naghdi, P. M.: The theory of plates and shells, in: Handbuch der Physik, Vol. VIa/2, pp. 425–460. Berlin-Heidelberg-New York: Springer 1972.
Libai, A., Simmonds, J. G.: Large-strain constitutive laws for the cylindrical deformation of shells. Int. J. Non-Linear Mech.16, 91–103 (1981).
Taber, L. A.: On approximate large strain relations for shell of revolution. Int. J. Non-Linear Mech.20, 27–39 (1985).
Green, A. E., Adkins, J. F.: Large elastic deformations. Oxford University Press 1970.
Biricikoglu, V., Kalnins, A.: Large elastic deformations of shells with the inclusion of transverse normal strain. Int. J. Solids Struct.7, 431–444 (1971).
Chernykh, K. F.: Nonlinear theory of isotropically elastic thin shells. Izv. AN SSSR Mekh. Tverdogo Tela15, 118–127 (1980).
Chernykh, K. F.: The theory of thin shells of elastomers. Advances in Mechanics6, 111–147 (1983), in Russian.
Pietraszkiewicz, W.: Lagrangian description and incremental formulation in the nonlinear theory of thin shells. Int. J. Non-Linear Mech.19, 115–140 (1983).
Stumpf, H.: On nonlinear buckling and post-buckling analysis of thin elastic shells. Int. J. Non-Linear Mech.19, (3), 195–215 (1984).
Stumpf, H.: General concept of the analysis of thin elastic shells. XVI. IUTAM-Congr-Lyngby, Denmark, 1984. ZAMM66, (6), 1–14 (1986).
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Stumpf, H., Makowski, J. On large strain deformations of shells. Acta Mechanica 65, 153–168 (1987). https://doi.org/10.1007/BF01176879
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DOI: https://doi.org/10.1007/BF01176879