Buckling and post-buckling behaviour of semicircular functionally graded material arches: a theoretical study

In this study, behaviour of a thin semicircular arch made of functionally graded material subjected to radial and tangential follower forces, as well as thermal loading, based on the theory of large deformation of the arches and critical buckling load and post-buckling of structures is investigated. Assuming thin arch, governing equations of the arch behaviour are derived using kinematics and static equilibrium. Resulting equations including different support conditions form a set of highly coupled and non-linear boundary value differential equations. To solve the problem, the well-known numerical boundary value problems of shooting method are employed. By gradual increase of loading, the buckling and post-buckling behaviour is closely monitored. Several examples corresponding to different combinations of support conditions/loadings/non-homogeneity/slenderness ratio to illustrate the performance of the proposed algorithm are presented.