NONLINEAR THEORY OF BENDING AND BUCKLING OF LOVE-KIRCHHOFF PLATES AND SHELLS
A general nonlinear theory of shells is derived from three-dimensional nonlinear elasticity theory and used to obtain exact linear perturbation equations for the determination of bifurcation points. These are specialized (1) to flat plates under inplane loading which preserves their flatness prior to buckling and (2) to shells of revolution which deform axisymmetrically under axisymmetric loading. The Love-Kirchhoff hypotheses for plates and shells are used. For the flat plate the strain-energy function is otherwise arbitrary, while for the shell of revolution the material must be either transversely isotropic or with axes of orthotropy coinciding with the shell generators and parallels. The specific example of a simply supported flat plate under uniform longitudinal compression, with the strain-energy function chosen as similar to that for small deformations of isotropic flat plates, is solved. Corrections to the classical theory are found to be of the same order of magnitude as those caused by shearing strains in planes normal to the middle surface. (Author)
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