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An incremental approach to the statement and solution of the problem of the nonlinear deformation of shells under loads that cause buckling and strong bending in the plastic range is developed. The relations between strains and displacements for great angles of rotation are used. A system of differential equations for the rates of the unknown functions is derived and represented in Cauchy operator form. To solve the boundary-value problem, the discrete-orthogonalization method is used assuming that the unknown functions and the loads are equivalent. The problem of the buckling and postbuckling behavior of a long D16T-alloy shell with a local initial deflection is solved as an example [ABSTRACT FROM AUTHOR]

In this study, out-of-plane stability analysis of tapered cross-sectioned thin curved beams under uniformly distributed radial loading is performed by using the finite-element method. Solutions referred to as Bolotin's approach are analysed for dynamic stability, and the first unstable regions are examined. Out-of-plane vibration and out-of-plane buckling analyses are also studied. In addition, the results obtained in this study are compared with the published results of other researchers for the fundamental frequency and critical lateral buckling load. The effects of subtended angle, variations of cross-section, and dynamic load parameter on the stability regions are shown in graphics [ABSTRACT FROM AUTHOR]

The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, or multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finite-element scheme. The method is justified numerically. Results of practical importance are obtained in analyzing poorely studied classes of inhomogeneous shells. These results provide an insight into the nonlinear deformation and buckling of shells under various combinations of thermomechanical loads. [ABSTRACT FROM AUTHOR]