Buckling of composite plate assemblies using higher order shear deformation theory—An exact method of solution

• The exact HSDT plate element has been shown to be extremely accurate.
• The exact HSDT plate element provides a significant refinement over to the FSDT one.
• The boundary conditions affect conspicuously the buckling modes.
• Stiffeners, if properly introduced increase the buckling load considerably.
• Stiffener position affects the buckling load significantly.

An exact dynamic stiffness element based on higher order shear deformation theory and extensive use of symbolic algebra is developed for the first time to carry out a buckling analysis of composite plate assemblies. The principle of minimum potential energy is applied to derive the governing differential equations and natural boundary conditions. Then by imposing the geometric boundary conditions in algebraic form the dynamic stiffness matrix, which includes contributions from both stiffness and initial pre-stress terms, is developed. The Wittrick–Williams algorithm is used as solution technique to compute the critical buckling loads and mode shapes for a range of laminated composite plates including stiffened plates. The effects of significant parameters such as thickness-to-length ratio, orthotropy ratio, number of layers, lay-up and stacking sequence and boundary conditions on the critical buckling loads and mode shapes are investigated. The accuracy of the method is demonstrated by comparing results whenever possible with those available in the literature.