Analysis of an initially stressed laminated plate based on elasticity theory

The governing equations of elasticity theory for natural vibration and buckling are derived from Hellinger–Reissner’s variational principle with nonlinear strain–displacement relations. Simply supported rectangular laminated plates based on exact theory of elasticity are studied by precise integration method. This method, in contrast to the traditional finite-difference approximation, gives highly precise numerical result, which approaches the full computer precision. So the results for natural vibration and buckling of cross-ply laminated plates, angle-ply laminated plates and hybrid plates presented in the paper can be regarded as analytical solutions. These results can be taken as a standard for both thin plates and moderately thick plates theory considering the effect of shear deformation. The several types of coupling effects, such as coupling between bending and twisting, coupling between extension and bending, etc. when the layer stacking sequence is not symmetric, are considered by only one set of governing equations.