Non-linear in-plane stability analysis of FG circular shallow arches under uniform radial pressure

• Non-linear stability analysis of FG shallow arches is performed in a closed-form method.
• Stability of FG shallow arches is investigated in the presence of pre-buckling deformations.
• Existence of bifurcation-type buckling is examined.
• A comprehensive study on the stability behavior of FG shallow arches subjected to uniform radial pressure is investigated.
• Influence of material distribution on the stability behavior of FG shallow arches is studied.

In this paper, non-linear stability behavior of functionally graded (FG) circular shallow arches subjected to a uniform radial pressure is investigated by an analytical method. For this purpose, the classical single layer assumption is used to approximate the displacement field through the arch. Donnell׳s non-linear model for shallow shells is employed to derive the strain–displacement relations. The material properties vary smoothly through the thickness of the arch according to a power-law distribution. The governing equilibrium equations and the complete set of boundary conditions are extracted employing the principle of virtual displacements and variational calculus. Because of considerable pre-buckling deformations of shallow arches, the stability analysis is accomplished considering the pre-buckling deformations. The non-linear equilibrium paths are presented for two symmetric types of boundary conditions. Results show the influences of properties dispersion, geometrical characteristics, and boundary conditions on the stability behavior of the FG circular shallow arches. Also, the results of the paper are compared with the known data in literature.