Bending analysis of functionally graded beam with porosities resting on elastic foundation based on neutral surface position

Abstract

In this paper, the Timoshenko beam theory is developed for bending analysis of functionally graded beams having porosities. Material properties are assumed to vary through the height of the beam according to a power law. Due to unsymmetrical material variation along the height of functionally graded beam, the neutral surface concept is proposed to remove the stretching and bending coupling effect to obtain an analytical solution. The equilibrium equations are derived using the principle of minimum total potential energy and the physical neutral surface concept. Navier-type analytical solution is obtained for functionally graded beam subjected to transverse load for simply supported boundary conditions. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. The influences of material parameters (porosity distributions, porosity coefficient, and power-law index), span-to-depth ratio and foundation parameter are investigated through numerical results. Keywords: functionally graded beam; bending analysis; porosity; elastic foundation; bending; neutral surface. Received 10 December 2018, Revised 28 December 2018, Accepted 24 January 2019