Static and buckling analyses of curved metallic and composite beams using hierarchical FEM

The conventional finite element formulation has limitations in performing the static and buckling analyses of composite curved beams. The hierarchical finite element formulation provides us with the advantages of using fewer elements and obtaining better accuracy in the calculation of displacements, stresses and critical buckling loads. The hierarchical finite element formulation for uniform curved beams made of isotropic and composite materials is developed in the present work. Two sub-formulations of hierarchical finite element method viz. polynomial and trigonometric sub-formulations have been developed. The efficiency and accuracy of the developed formulation are established in comparison with the closed form solutions for uniform isotropic and composite curved beams. The central deflection values of uniform isotropic and composite curved beams are evaluated using the hierarchical finite element method. The critical buckling loads of composite curved beams are calculated based on the developed formulation and the results are validated with the approximate solution by the Ritz method. A detailed parametric study encompassing the influences of boundary conditions, laminate configuration, and the internal degrees of freedom is performed to see their effect on the central deflection and the critical buckling load. The NCT-301 graphite-epoxy composite material is considered in the analysis and in the parametric study