Exact solution of a geometrically nonlinear problem for a long three-layer cylindrical panel of oval section

Abstract

A statement is given and an exact solution of a geometrically nonlinear problem is given for a long open three-layer cylindrical shell of an oval cross-section susceptible to transverse shear under the action of a uniform surface load. The main equations are written according to the geometrically nonlinear theory of smooth shells in the quadratic approximation, in which Tymoshenko's hypotheses hold for the entire package of shell layers. The solution of the problem is obtained in a parametric form with the value of the tangential force as a parameter. For a shell with hinged longitudinal edges, the exact values of the components of the stress-strain state were obtained, the limit values of the generalized geometric parameter were determined, and a system of equations for finding the critical load was constructed. As partial cases, the obtained solution yields the corresponding results for the Kirchhoff–Leav model, the shell of a circular cross-section, and the single-layer shell. The obtained results can be a reference for approximate and numerical methods.