Abstract
In this article we present an exact and systematic derivation of a theory of finite strain deformation of shells from the principles of classical continuum mechanics. We assume that the three-dimensional deformation of the shell satisfies the following kinematical constraints; I) material fibres initially normal to the reference surface of the shell remain straight during the deformation, II) deformation is isochoric (volume preserving). These are the only assumptions made in our developments out which the first one is of simplifying nature while the other one reflects merely the real property of many materials. We show that the resulting theory is characterized by the following features; a) a rational incorporation of transverse shear deformation and exact incorporation of transverse normal deformation, b) the constitutive equations for the stress resultants and stress couple as nonlinear functions of appropriate strain measures and their surface derivatives, c) a sufficient geometric structure to account for a non-uniform change in the shell thickness at the boundary.
Part of the paper has been written during the author’s stay at Ruhr — University
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References
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© 1986 Springer-Verlag Berlin, Heidelberg
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Makowski, J., Stumpf, H. (1986). Finite Strains and Rotations in Shells. In: Pietraszkiewicz, W. (eds) Finite Rotations in Structural Mechanics. Lecture Notes in Engineering, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82838-6_14
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DOI: https://doi.org/10.1007/978-3-642-82838-6_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16737-2
Online ISBN: 978-3-642-82838-6
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