Non-linear in-plane stability analysis of FGM circular shallow arches under central concentrated force

• Non-linear stability analysis is performed in a closed-form analytical method.
• Stability of FGM shallow arches is investigated in the presence of pre-buckling deformations.
• Existence of bifurcation-type instability is examined in detail.
• A comprehensive study on the stability behavior of FGM shallow arches under central concentrated load is investigated.
• Influence of material distribution on the stability behavior is studied.

A comprehensive study on the non-linear in-plane stability behavior of shallow arches made of functionally graded materials (FGMs) is presented in this work. Simply supported–simply supported (S–S) and clamped–clamped (C–C) boundary conditions are considered as two types of well-known symmetric boundary conditions for this analysis. The arch is subjected to a central concentrated force and material dispersion is according to the power law distribution. For this aim, the classical single layer theory is adjusted to approximate the displacement field through the arch. Kinematical relations are reduced to suitable ones for shallow arches. Static version of the virtual displacement principle is used to obtaining the governing equations and the complete set of boundary conditions. In the presence of the highly non-linear behavior of shallow arches under central concentrated force, buckling analysis is preformed in the presence of pre-buckling deformations. Existence of secondary equilibrium paths for shallow arches is studied and stability behavior of FGM shallow arches is classified into non-linear bending, full snap-through, bifurcation from post-snap path, and bifurcation. Also, multiple snap-to-state condition is investigated for FGM shallow arches. Results are presented as primary equilibrium paths and effect of material dispersion, geometrical characteristics, and boundary conditions on the stability behavior of shallow arches under central concentrated force is studied.