Mixed formulation for sensitivity analysis of laminated conical shells

A mixed formulation has been proposed to simplify the calculation of initial postbuckling behavior and Koiter's b parameter for laminated shells. According to Koiter's general theory of elastic stability, the imperfection sensitivity of a structure is closely related to its initial postbuckling behavior, and the theory is exact in the asymptotic sense. The nonlinear equilibrium equations and the appropriate boundary conditions are derived on the basis of the potential-energy approach. The classical buckling load of a perfect structure is denoted which is the load at which a nonaxisymmetric bifurcation from the prebuckling state occurs. This method's advantages include direct involvement of the stiffness matrices, without their derivatives, exclusive linear and quadratic operators in the governing equations, and the first derivatives in the axial direction of the unknown functions the highest. These features make for a much simpler and more accurate analysis of the shell's behavior, which can be applied to any shells of revolution for the analysis of both initial postbuckling and full nonlinear behavior.