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An approach to solving the problem of the nonlinear deformation of orthotropic cylindrical shells is proposed. On the surface of the shell, there is a local deflection bounded by segments of the coordinate lines. The Timoshenko-Mindlin shell theory, the Byskov-Hatchinson asymptotic method, and the continuous continuation method for solving nonlinear algebraic equations are used. To determine the critical loads and deformation paths, it is necessary to estimate the number of interacting modes sufficient to achieve satisfactory accuracy. Examples of analyzing composite shells with an initial local deflection of positive or negative amplitude are given [ABSTRACT FROM AUTHOR]

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]

The fundamentals of the reduced-stiffness method, which is used in buckling analysis of reinforced and perfect and imperfect nonreinforced shells, are set out. The method is validated analytically and experimentally. The lower bound determined by this method is very close to the experimental lower bound. Some aspects of the current state and prospects for development and generalization of the method are discussed. [ABSTRACT FROM AUTHOR]