Investigation of strength and buckling of orthotropic conical shells and conical panels

In the construction, thin-walled shell structures are used to cover the buildings of large areas, such as stadiums, hangars, circuses, airports. In this paper, the strength and buckling of closed conical shells as well as their panels are studied. The geometric nonlinearity and transverse shifts are taken into account. A mathematical model is used in the form of a functional of the total potential energy of deformation. Also expressions for deformations, forces and moments are given. The calculation program is implemented in the MatLab environment. The algorithm is based on the Ritz method and Newton's method for solving a system of nonlinear algebraic equations. Variants of approximating functions for a closed shell and for its panel are shown. The values of critical loads are found, the dependence of the deflection on the load, the dependence of the stresses on the load is obtained, and the deflection field is shown at the subcritical and at the supercritical moment. The fields of various stress components are given at the moment when the strength conditions begin to fail. The orthotropy of the material is taken into account.