Postbuckling behavior of symmetrically laminated thin shallow circular arches

The large deflection behavior of a symmetrically laminated thin shallow circular arch subjected to a central concentrated load is studied using the Rayleigh–Ritz finite element method. The shape functions used in the finite element method maintain C1-continuity of the radial displacement (deflection) and C0-continuity of the tangential displacement, respectively.The nonlinear algebraic equations of equilibrium are solved to a high degree of accuracy using Taylor’s expansion technique in conjunction with the Newton–Raphson method. Nonlinear stability analysis provides accurate solutions for the symmetric and antisymmetric buckling of both pin-ended and fixed shallow arches. The stability of the symmetric deformation path is investigated for both pinned and fixed arches, and a detailed analysis is carried out at the point of bifurcation onto an asymmetric deformation path for a pinned symmetrically laminated shallow arch. The slope of this post-buckled path is also computed, and is shown to be accurate for deformations well beyond the point of bifurcation.