Closed-form buckling analysis of compressively loaded composite plates braced by omega-stringers

In this contribution, the stability problem of composite plates braced by longitudinal omega-stringers under compression is treated in a closed-form analytical manner. Given that no global buckling modes of both plate and stringers occur and further assuming certain periodicity properties of the occurring local plate buckling modes, the given situation is reduced to the bifurcation buckling problem of an elastically restrained plate wherein the edge restraints depend on the geometric and material properties of the stringers and are calculated via the principle of virtual work. The buckling modes of the plate itself are approximated using an interpolation scheme consisting of rather simple trigonometric functions which allows for a closed-form analytical description of both the buckling modes as well as of the buckling loads of the elastically restrained composite plates. Accompanying detailed finite element computations show that the closed-form analytical approach is in very satisfying agreement with the numerical results and as such can be used with confidence in day-to-day engineering practice. Furthermore, the exact elasticity solution for the buckling problem of a compressively loaded elastically restrained composite plate is shortly discussed which can be derived from the governing partial differential equation in conjunction with the underlying boundary conditions of the plate. The closed-form approach can be shown to be in excellent agreement with the exact results which are generated in a numerical manner. Lastly, based on non-dimensional characteristic quantities, the exact elasticity solution is used to generate generic buckling curves which may be useful for practical engineering analysis and design purposes.