Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 43 2 2012 02 20 Large deflection of Flexible Functionally Graded Beams with Geometric Non-linearity: Analytical Approach Large deflection of Flexible Functionally Graded Beams with Geometric Non-linearity: Analytical Approach 9 17 65 10.22060/mej.2012.65 FA Ali Reza Davodi Nik Gholamhosein Rahimi Sherbaf Journal Article 2014 03 15 Motivation of this paper is presentation of analytical solution for flexible functionally graded beams problem when carry elastic large deflection, with small strains and without concerning plastic region. The formulation of large deflection in curvilinear and Cartesian coordinate systems for the free-clamped flexible functionally graded beam, culminate in the second order non-linear ordinary differential equation that can solve it in the analytical approach. The components of deflection that are derived with analytical solution and ANSYS approach are compared. The influence of the distribution reversing of the material property and the influence of the variable material property in the components of deflection are studied. This analytical approach can be used for verifying the other method results, if any. Motivation of this paper is presentation of analytical solution for flexible functionally graded beams problem when carry elastic large deflection, with small strains and without concerning plastic region. The formulation of large deflection in curvilinear and Cartesian coordinate systems for the free-clamped flexible functionally graded beam, culminate in the second order non-linear ordinary differential equation that can solve it in the analytical approach. The components of deflection that are derived with analytical solution and ANSYS approach are compared. The influence of the distribution reversing of the material property and the influence of the variable material property in the components of deflection are studied. This analytical approach can be used for verifying the other method results, if any. https://mej.aut.ac.ir/article_65_658b798a12657f884c1d2977ce87270f.pdf