Analysis of nonlinear deformation and stability of oval cylindrical shells under combined loading by bending and torsion moments

Abstract

A problem of geometrically nonlinear deformation and stability of cylindrical shells with noncircular cross-section contour is solved by the finite element method. The nonlinear system of algebraic equations to determine the nodal unknowns of finite elements is obtained with the use of the variational Lagrange principle. The system is solved by the method of successive loadings with the use of the Newton-Kantorovich method of linearization, the method of solving linear Craut’s equations and Sylvestor’s stability criterion. The nonlinear deformation and stability of shells with the oval and elliptical cross-sections under combined loading by bending and torsion moments are analyzed. The critical loads and buckling modes of shells are determined. The influence of deformation nonlinearity, shell ovality and ellipticity on the critical loads is clarified.