Lateral-torsional buckling of functionally graded porous arches with graphene platelets reinforcements under an arbitrary radial concentrated load

This paper investigates the lateral-torsional buckling of functionally graded porous (FGP) circular arches with an I-section made of graphene platelets reinforced composites (GPLRC) under an arbitrary radial concentrated load, which has not been reported in open literature so far. The effective elastic modulus of the FGP- GPLRC arches is estimated by the Halpin-Tsai micromechanics model. After pre-buckling internal forces caused by the concentrated load have been obtained, the principle of stationary potential energy and Rayleigh-Ritz method are employed to derive theoretical solutions for the lateral-torsional buckling loads of FGP-GPLRC arches based on Timoshenko beam theory. The present theoretical solutions for the buckling loads are validated against the finite element results. The analytical expression of the effective warping stiffness and torsional stiffness of FGP-GPLRC arches are then obtained by an integral method. Finally, the influences of pore distribution pattern, porosity coefficient, weight fraction of graphene platelets (GPLs), load position, include angle and slenderness ratio of the arch on the lateral-torsional buckling load are analyzed in detail. Results show that a higher porosity coefficient leads to lower buckling loads but an increase in GPL weight fraction can effectively enhance the buckling resistance of the arch. Compared with their counterparts with uniform or asymmetric porosity distribution, FGP-GPLRC arches with symmetric non-uniform porosity distribution have higher lateral-torsional buckling loads.