A higher order finite element theory for buckling and vibration analysis of initially stressed composite sandwich plates

A simple isoparametric assumed strain finite element formulation incorporating a third-order polynomial displacement model for the buckling and vibration analysis of initially stressed composite sandwich laminates is presented. The displacement model involves a nonlinear distribution of in-plane displacements through the plate thickness; the theory does not require shear correction coefficients. A nine-noded quadratic Lagrangian two-dimensional element is used with three displacements, two rotations of the normals about the plate midplane, and two warps of the normals. Full integration is carried out to evaluate various terms in the energy formulation. A consistent mass matrix is employed to preserve the total kinetic energy of the system. The accuracy of the present formulation is verified with the existing results in the literature. Numerical results are presented for the stability and free vibration of initially stressed composite sandwich plates.