Localised formulations for thick “sandwich” laminated and composite structures

A “sandwich” panel under axial compressive loading is studied over its post-buckling range. Alternative formulations were developed to cover solutions other than the deflection shape given by the classical Rayleigh-Ritz analysis. General elasticity principles are used to derive the total potential energy function in terms of the displacement field. Given a constant modal amplitude displacement field, which is introduced in the total potential energy function, the results are discussed having as background models studied earlier. Techniques for the analysis of localized solutions are presented with reference to the study of the beam on nonlinear elastic foundation. The concepts of localization are introduced by using dynamical analogy and the double scale perturbation method and applied to the sandwich panel, to derive the governing amplitude modulation equations. The resulting formulations are discussed using some examples, and by solving analytical and numerically the amplitude differential equations.