INPLANE BUCKLING OF ANISOTROPIC RINGS

Abstract eng:
Inplane buckling of laminated rings is considered based on a non-linear theory for stretching and bending of geometrically and materially symmetric anisotropic beams having constant initial curvature in their plane of symmetry. The ring is formed by initially curving the laminated beam out of the plane of the laminate. For the kinematics, the geometrically exact one-dimensional (1-D) measures of deformation are specialized for small strain, and a 1-D constitutive law is developed via an asymptotically correct dimensional reduction of geometrically non-linear 3-D elasticity. The reduction assumes small strain and comparable magnitudes for the initial radius of curvature R and the wavelength of deformation along the beam reference line. Other small parameters include the ratio of cross-sectional thickness h to initial radius of curvature (h/R) and the ratio of cross-sectional thickness to cross-sectional width (h/b). In spite of a very simple final expression for the second variation of the total potential, it is shown that the only restriction on the validity of the buckling analysis is that the prebuckling strain remains small. The buckling load obtained exhibits features not found in published formulae.

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