Postbuckling of FGM rings

• Closed form solutions are obtained for the critical buckling pressure of FGM rings.
• Non-linear adjacent equilibrium criterion is applied to trace the post-buckling path.
• GDQM is applied successively to the nonlinear stability equations.
• An FGM ring that is subjected to hydrostatic pressure is imperfection insensitive.

Buckling and post-buckling behaviors of a moderately thick closed ring made of a through-the-thickness functionally graded material (FGM) is investigated in this research. It is assumed that material properties of the ring are distributed across the thickness in terms of a power law model. The first order theory of shear deformable rings along with the von Kármán type of geometrical non-linearity is incorporated with the virtual displacements principle to establish the complete form of the coupled non-linear equilibrium conditions. The analysis is restricted to the case of hydrostatic pressure. An exact closed-form solution is developed to trace the pre-buckling deformations of the ring. Non-linear adjacent equilibrium criterion, which is an efficient criterion to deduce the post-buckling path, is implemented to establish the highly non-linear coupled stability equations. The generalized differential quadrature (GDQ) method is adopted to discrete the equilibrium equations and the associated boundary conditions. Numerical illustrations cover the post-buckled shape and deflection of the ring in the intermediate post-buckling regime. It is shown that, unlike the case of the flat beams, response of closed FGM rings is similar to the case of isotropic homogeneous ring. Consequently, hydrostatically loaded FGM rings exhibit the imperfection insensitivity feature through the loading process.