Nonlinear buckling and post-buckling analyses of functionally graded circular shallow arches

Abstract

Snap-through analysis of thin, functionally graded (FG), fixed, circular shallow arches subjected to uniformly distributed vertical load is examined in this paper. The modulus of elasticity varies gradually along with the normal to the axis of the arch in alliance with the power law form. The solution of the geometrically nonlinear problem is carried out by using a numerical scheme accounting for the moderately large deflections theory based on small strain and moderate rotation in the von Kármán sense. The combined effect of the parameters that is, the power law index, the ratio of the modulus of elasticity and the modified slenderness ratio on the support reactions, the snap-buckling and post-buckling behaviors of the fixed circular shallow arches are examined. It is found that the lowest buckling load is considerably affected by the variation of these parameters. In addition, the effects of the material distribution on internal forces, deformed configurations and rotation angle are presented at various stages of the deformation.