Abstract
Abstract There is considered the problem of loss of stability of thick-walled cylinders subjected to inhomogeneous initial stresses. The analysis is based on the exact threedimensional equations of neutral equilibrium problems derived by superposing small on finite deformations. The law of the state is determined by a five-constant Murnaghan relationship. Cases are studied of the buckling of circular cylinders subjected to axial load and side internal and external hydrostatic pressure. Results are represented for calculations exhibiting the influence of nonlinearity on the upper critical load as a function of the geometric parameters. There exists a comparatively small number of papers in which the stability of equilibrium is investigated on the basis of the three-dimensional equations of nonlinear elasticity theory /1/. Results are obtained for bodies of simple shape (slab, rod, hollow sphere, cylindrical tube), in which most solutions rely on a simplifying hypothesis regarding the incompressibility of the material or an assumption regarding the simple form of the state function. Mainly cases of neo-Hookean and semilinear materials are studied /2,3/.
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