On the statics of fullerene structures

In the present study, thorough research on bending analysis of the fullerene structures (such as C-60, C-720,C- C-2160, and C-4860) resting on the Winkler-Pasternak elastic foundation and under external loading is conducted. Small-scale effects on the results are taken into consideration via nonlocal elasticity theory. The geometry of fullerene structures is assumed as a sphere and doubly-curved structure. The static governing equations for fullerene structures are derived by implementing the principle of minimum potential energy on the basis of the nonlocal first-order shear deformation theory. Various types of boundary conditions including the free edges are considered. The elastic foundation is applied locally on the particular area of the structure, on the contrary of the most available researches that have considered it on the whole of problem geometry. For this aim, an innovative formulation is presented in which simulates the elastic foundation locally. The resulting equations are solved by using the semi-analytical polynomial method (SAPM). Since no similar research has been done before, the bending results of a spherical structure (whereas the fullerene structure can be approximated by a sphere) are compared and validated with the results of ABAQUS software. Also, the effects of several important parameters such as the type of fullerene structure, the nonlocal parameter, and the elastic foundation constants on the results are investigated in detail. (C) 2019 Elsevier Ltd. All rights reserved.