Nonlinear in-plane instability of the confined FGP arches with nanocomposites reinforcement under radially-directed uniform pressure

Abstract

The nonlinear buckling of the functionally graded porous (FGP) arches with nanocomposites reinforcement is studied in this paper. Both the pores and the nanocomposites are distributed symmetrically to the mid-axis of the cross-section. When the arch is encased in the elastic medium, the deformed shape of the arch can be described as a “single-lobe”, which can be expressed precisely by a cosine displacement function. By employing the nonlinear thin-walled shell theory and the principle of minimum potential energy, an analytical solution of the loading capacity is obtained, which is examined by developing a three-dimensional (3D) simulated model. After introducing the geometric nonlinearities and the Riks technique, the maximum load (loading capacity) is obtained numerically. Both the analytical and numerical results are successfully compared and verified by other closed-form expressions. It is found that the pores reduce the loading capacity, while a small addition of the nanocomposites increases prominently the loading capacity of the FGP arches. The confinement effect is examined by comparing the loading capacity between the confined and unconfined arches. The results indicate that the confinement effect increases with the increase of the central angle. Finally, parametric evaluations are taken to examine the effects of geometric shapes of the nanocomposites and interface friction on the loading capacity of the FGP-GPLs arches.