Minimum stringer stiffness of shear deformable composite laminated plates for maximum buckling performance

Abstract This paper presents a closed-form analytical approach to the buckling behavior and stringer design of stiffened composite plates under uniaxial compressive load wherein the influence of transverse shear deformations is taken into account explicitly. For this purpose, besides classical laminated plate theory, first-order and third-order shear deformation theory are employed. First, a closed-form solution is derived for the global buckling load of the stiffened plate, i.e., when plate and stringer buckle simultaneously. The solution is based on simple shape functions for the buckling mode in conjunction with the principle of the total elastic potential of the plate in the buckled state. Furthermore, a solution for the local buckling load is presented which is derived in a similar manner as the global solution. Lastly, a criterion for the determination of the minimum bending stiffness of the stringer is derived, i.e., a closed-form expression for the bending stiffness that is required to enforce a local buckling mode. Results for centrically and excentrically stiffened plates are presented which highlight the importance of the consideration of transverse shear deformations for thick to moderately thick plates, and comparative finite element computations show that the developed analysis approaches work with good accuracy and yet negligible computational effort.