An analytical solution to estimate the critical buckling load of doubly-curved laminates under a combined load of uni-axial compression, in-plane shear and bending moment

Curved panels are structural elements that form the skin of wings, fuselages and tail booms in aircraft. Buckling of these structures would adversely affect aircraft performance. Due to this, the problem of buckling has been extensively researched in the past. Most of the research has been restricted to the analysis of flat composite panels and analysis of curved panels through simplifications involving geometry, material properties and boundary conditions. The present study aims to develop an analytical solution that can predict the critical buckling load for a wider range of problems. An analytical solution was developed in order to obtain the critical buckling load for a doubly-curved composite laminate under compression, shear, moment or any combination of the three loads. The assumptions of the classical laminate plate theory were used in order to obtain the displacement fields as well as strains of the laminate. The energy method was employed in order to obtain the critical buckling load for various load cases. The values obtained through the analytical solution are compared to the critical buckling loads obtained through finite element analysis (FEA). The highest deviation of critical buckling load from FEA was calculated to be 16.55%. Variation of the critical buckling load with respect to the radius of curvature, boundary conditions and stacking sequence was analyzed. The developed solution was also found to be valid for cases when radii of curvatures are unequal as well as when the length and breadth of laminate are unequal.