Homotopic analysis for post-buckling of cylindrical shells with local thickness defects

A post-buckling model of cylindrical shells with local thickness defects is established based on the Hamiltonian system. The homotopy analysis method and the symplectic eigensolution expansion method are combined to obtain the post-buckling equilibrium path and post-buckling modes of the cylindrical shells with defects. By constructing an eigenvalue buckling problem of the defective cylindrical shell as a zero-order homotopy deformation equation, a significantly better convergence rate can be obtained when compared to the classical perturbation method. The result shows that the defects can induce unique local dents and significantly reduce the ultimate post-buckling bearing capacity of the cylindrical shells. The research finds important and practical applications in many engineering fields that use cylindrical shells as key design components, in particular in aerospace and aeronautical engineering, marine engineering, automobiles, civil engineering, etc.