Abstract
An application of a moderate rotations theory (MRT) to cylindrical elastic-plastic shells is presented. Geometrical and kinematical relations for cylindrical shells with arbitrary cross-section are derived. Following the general procedure formulated in [4] we derive also equilibrium equations for cylindrical shells. Some special cases of loading and cross-section shapes of shells are discussed in more details. Orthotropic elastic-plastic constitutive relations are assumed and expressed in terms of a cylindrical reference frame. In a forthcoming paper we are going to apply these results as a basis for numerical solving of geometrically nonlinear problems for cylindrical shells.References
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8. K. HACKL, A framework for nonlinear shells based on generalized stress and strain measures, Int. J. Solids Struct., 34, 1997.
2. M. DUSZEK, Foundations of the non-linear plastic shell theory, Mitt. Inst. Mechanik, Ruhr-Universität, Bochum, 31, 1982.
3. K.W. NEAL, A general variational theorem for the rate problem in elasto-plasticity, Int. J. Solids Structures, 8, 1972.
4. R. SCHMIDT, D. WEICHERT, A refined theory of elastic-plastic shells at moderate rotations, ZAMM, 69, 1, 1989.
5. J.C. SIMO et al., On a stress resultant geometrically exact shell model, Parts I-IV, Comp. Meth. Appl. Mech. Engng., 72, 73, 1989, 79, 81, 1990.
6. A. SŁAWIANOWSKA, A comparison of two theories of geometrically nonlinear shells, J. Theor. Appl. Mech., 34, 4, 1996.
7. K. WASHIZU, Variational methods in elasticity and plasticity, Pergamon Press, 1975.
8. K. HACKL, A framework for nonlinear shells based on generalized stress and strain measures, Int. J. Solids Struct., 34, 1997.
