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On the axisymmetric buckling behaviour of incompressible nonlinearly elastic spherical shells
Author(s) -
Labisch F.K.
Publication year - 2006
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200410266
Subject(s) - buckling , quasistatic process , compressibility , bifurcation , rotational symmetry , hydrostatic equilibrium , hydrostatic pressure , bifurcation theory , mechanics , spherical shell , shell (structure) , shear (geology) , classical mechanics , materials science , geometry , physics , mathematics , nonlinear system , composite material , thermodynamics , quantum mechanics
Abstract In this paper we study the axisymmetric quasistatic buckling behaviour of complete incompressible nonlinearly elastic spherical shells under hydrostatic pressure. The shells suffer flexure, shear, and mid‐surface compression. Thickness changes occurring on the trivial solution are taken into account. The theory is geometrically exact; the description is based on a 3‐dimensional model with an involved thickness parameter δ. The approach yields the pressure intensities at which bifurcation branches emanate, provides information about the qualitative and quantitative local solution behaviour and permits in some neighbourhood of the trivial solution a determination of the deformed shell configuration associated to the bifurcation modes. Numerical results are presented.