Stress analysis of functionally graded nanobeams using hyperbolic theory

Abstract

This study uses the hyperbolic nonlocal theory in conjunction with Eringen's nonlocal theory to analyze the bending of nanobeams. The proposed theory incorporates constitutive relations to ensure zero shear stress conditions at the top and bottom surfaces of the nanobeam. The equations of motion are derived using Principle of work-done.The developed theory is then employed to analyze nanobeams made of functionally graded materials. To solve the problems, the Navier technique is utilized. In order to assess the accuracy of the proposed theory, numerical results are compared with those obtained from other existing theories, namely the third shear deformation theory of Reddy, the first-order shear deformation theory of Timoshenko, and the classical beam theory of Bernoulli-Euler, all of which account for nanosize effects.The comparison of results demonstrates that the outcomes obtained from the hyperbolic nonlocal theory align well with those obtained from higher-order theories. This indicates that the proposed theory provides a reliable and accurate approach for analyzing the bending behavior of nanobeams, incorporating the effects of nanosize.