Assessments of the non-linear instability of arches with imperfect geometry

The article addresses the static in-plane instability of shallow arches. The model takes account of arbitrary geometrical imperfections as initial displacements that cause strain. A geometrically non-linear formulation is presented with the effect of the bending moment on the membrane strain incorporated. The model uses the single layer theory and is applicable also for functionally graded material distributions along the cross-sectional height. Coupled equilibrium equations are found from a variational principle which are solved analytically. Comprehensive studies focus on the influence of symmetric and anti-symmetric geometrical errors on the in-plane behaviour and stability of arches. The imperfection mode and magnitude can have potentially positive and negative effects too on the critical load. Depending on the geometrical properties of the arch, the shape error can significantly influence the bending moment or the axial force distribution along the arch centroidal axis.