A novel hyperbolic shear deformation beam theory for functionally graded nonlocal nanobeams

This paper introduces an innovative nonlocal hyperbolic shear deformation theory for the bending, buckling, and vibration analysis of functionally graded (FG) nanobeams. The theory is developed based on a displacement field that accounts for both bending and shear components, ensuring accurate modeling of transverse shear deformation without requiring shear correction factors. Using Hamilton’s principle, the governing equations are derived, and closed-form solutions for deflection, buckling load, and natural frequency are obtained for simply supported nanobeams. The outcomes reveal that the proposed theory provides significantly more accurate results than classical beam theories such as Euler–Bernoulli and Timoshenko beam theory, especially in capturing the effects of material gradation and nanoscale behavior. Numerical results demonstrate that the inclusion of the shear component leads to a better understanding of critical buckling loads and the natural frequencies of FG nanobeams, validating the superiority of the proposed model in nanoscale structural analysis. The findings also indicate the importance of material gradation in influencing the mechanical response, making the theory a valuable tool for the design and analysis of FG nanostructures.