Nonlinear buckling of thin-walled FGM arch encased in rigid confinement subjected to external pressure

This paper investigates the buckling of confined thin-walled functionally graded material (FGM) arch subjected to external pressure. The confined FGM arch buckles in a single-lobe deformation expressed by an admissible radial displacement function. The critical buckling pressure of the confined FGM arch is obtained analytically by establishing the nonlinear equilibrium equations based on the classical thin-walled arch theory. Subsequently, a two-dimensional (2D) finite element model (FEM) is established to trace the pre- and post-buckling equilibrium paths. Geometric nonlinearities are introduced since large displacement and rotation occur during the whole deformation of the FGM arch. The numerical results show very close agreement with the present analytical solutions in terms of the hoop force through the FGM arch span, the critical buckling pressure, and the pressure displacement equilibrium paths. Furthermore, the present predictions are compared successfully with other closed-form expressions for the confined homogeneous arch. Finally, the effect of volume fraction exponent on the buckling pressure, the hoop force and bending moment through the arch span is examined and discussed to further understand the budding behavior of the confined FGM arch.