Hamiltonian system and post buckling of elastic cylindrical shells under the heat shock

Based on the Donnell theory, thermal elasticity, large deflection theory and energy principle, a Hamiltonian system was presented for the buckling of shells under thermal shock. The buckling problem was divided into two stages, namely, pre-buckling and post-buckling. In the Hamiltonian system, generalized eigenvalues and symplectic eigensolution correspond to critical temperatures and buckling modes, respectively. Based on symplectic eigensolutions, computational formulas for post-buckling of shells under thermal shock were derived using adjoint symplectic orthogonality and symplectic expansion theorem. Thus, a numerical method is formed. The numerical results describe the whole process of buckling development for cylindrical shells. The results show that the post buckling evolvement depends highly on the source location, distribution, boundary conditions, intensity of heat source, material parameters, and geometrical shape of shells. Besides, the buckling mode is developing from lower to higher order and finally tends to vibration mode.