Longitudinal and transverse bending on the cylindrical shape of a sandwich plate reinforced with absolutely rigid bodies in the front sections

A geometrically nonlinear problem of longitudinal and transverse bending on the cylindrical shape of a sandwich plate with transversally soft core reinforced in the front sections by absolutely rigid bodies intended to ensure the transfer of load to the carrier layers when they interact with other structural elements has been considered. The equations of the refined geometrically nonlinear theory, which allow one to describe the process of their precritical deformation and to reveal all possible buckling forms of the carrier layers (in-phase, antiphase, mixed bending and mixed bending-shear, and also arbitrary, including all of the above) have been used. These equations have been derived by introducing the contact forces of the interaction of the outer layers with the filler, as well as those of the outer layers and the filler with the reinforcing bodies at all points of the surfaces of their conjugation, as unknown parameters. A numerical method for solving the formulated problem has been developed. The method has been constructed by preliminary reduction of the problem to a system of integro-algebraic equations solved with the help of the finite-sum method. A method has been developed for studying the precritical geometrically nonlinear behavior of the plate as a result of its front compression through a reinforcing body. The results of the numerical experiments have been presented and analyzed.