Post buckling analysis of shallow composite shells based on the third order shear deformation theory

In the present paper, a higher-order shear deformation theory of elastic shells was developed for geometrically nonlinear analysis of laminated shells of orthotropic layers. The theory can better represent the kinematics, may not require shear correction factors and can yield more accurate interlaminar stress distributions. The nonlinear mathematical model is derived using the Green-Lagrange type geometric nonlinearity in the framework of the higher order shear deformation theory. The developed model accounts for parabolic distribution of the transverse shear strains through the thickness and tangential stress-free boundary conditions on the boundary surfaces of the shell. Therefore, shear correction factors of the usual shear deformation theory are not required in the present theory. The principle of the virtual work forms the basis to derive the nonlinear finite element equations. The nonlinear equilibrium equations are solved using an incremental iterative technique based on the arc length method.