Abstract
In this paper we study the global qualitative behavior of axisymmetric buckled states of homogeneous isotropic nonlinearly elastic shells that can suffer flexure, compression, and shear. Our model is geometrically exact in the sense that a geometric quantity, such as sin θ, is not replaced by an approximation, such as θ or θ — θ 3/6. (The usual justification for such a replacement is that θ is known to be small for the physical situation under study. But it is quite possible that a mathematical model with exact geometry permits only small solutions, while those with approximate geometry have large solutions.) We allow the material properties to be described by a very general class of nonlinear constitutive relations. Consequently our governing equations form a quasilinear sixth-order system of ordinary differential equations.
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This paper is dedicated to James B. Serrin on the occasion of his sixtieth birthday
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© 1989 Springer-Verlag Berlin Heidelberg
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Shih, KG., Antman, S.S. (1989). Qualitative Properties of Large Buckled States of Spherical Shells. In: Analysis and Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83743-2_11
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DOI: https://doi.org/10.1007/978-3-642-83743-2_11
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