A Symplectic Analytical Approach for Torsional Buckling of Cylindrical Shells with Asymmetric Local Defects

Abstract

A torsional buckling model of cylindrical shells with asymmetric local thickness defect is established based on the Hamiltonian system. The critical load and torsional buckling mode of cylindrical shells with defects are obtained by the symplectic eigensolution expansion method, which overcomes the difficulty of constructing the deflection function of the traditional semi-inverse method. Local buckling modes can be captured by this new analytical model with the superposition of symplectic eigensolutions. To ensure accuracy and validity of the symplectic method, the analytical solution with torsional buckling of a cylindrical shell is compared with the classical solution and the finite element method (FEM) solution. The results show that the most detrimental position of the defect is only related to the width of the defect, not to the depth. The local defect changes the circumferential buckling wave number of the cylindrical shell and concentrates the torsional corrugation on the side containing the defect. Torque symmetry is broken due to the asymmetric defect, and the most detrimental defect direction for buckling is the same as the direction of torsional buckling wavelet.