Stability of the Cantilever Elliptical Composite Cylindrical Shell during Transverse Bending

The problem of stability of non-circular elliptical cylindrical shells made of composite material is solved, taking into account the momentarity and nonlinearity of their subcritical stress-strain state. The geometrically nonlinear stability problem is solved by finite element methods and Newton–Kantorovich linearization. Critical loads are determined in the process of solving a nonlinear problem using the Sylvester criterion. The finite elements of composite cylindrical shells of natural curvature, developed on the basis of the Timoshenko hypothesis, are used, and their rigid displacements are explicitly highlighted in the approximation of their displacements, which significantly affects the convergence of the solution. The stability of an elliptical, cantilever-mounted cylindrical shell made of a polymer composite material is investigated when loaded with an edge transverse force. The influence of the monolayer laying methods, the nonlinearity of deformation, and the ellipticity parameter on the critical loads of shell stability loss and weight efficiency of composite shells was clarified.