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<p>An analytical solution for the large deflection static bending of nanobeams is developed based on Gurtin–Murdoch continuum theory, which accounts for surface energy effects. According to this theory, the surface of a nanobeam is modeled as a mathematically deformable membrane of zero thickness, fully adhered to the underlying bulk material. The Euler–Bernoulli beam theory, incorporating surface effects, is used to derive the governing differential equation for large deformation bending of nanobeams. The analytical solutions for the nonlinear differential equation of nanobeams under a concentrated load are obtained using the homotopy analysis method (HAM). Results are presented for nanobeams with clamped-free, simply supported, and clamped–clamped, boundary conditions. The obtained analytical solutions show good agreement with numerical methods reported in the literature. The effects of surface stresses on the bending behavior of silicon nanobeams are investigated using the developed solution method.</p>

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A homotopy analysis solution for large deformation bending of nanobeams based on surface effect theory

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Mehran Hajalizadeh,
  • Hossein Baradaran,
  • Reza Bahaadini

摘要

An analytical solution for the large deflection static bending of nanobeams is developed based on Gurtin–Murdoch continuum theory, which accounts for surface energy effects. According to this theory, the surface of a nanobeam is modeled as a mathematically deformable membrane of zero thickness, fully adhered to the underlying bulk material. The Euler–Bernoulli beam theory, incorporating surface effects, is used to derive the governing differential equation for large deformation bending of nanobeams. The analytical solutions for the nonlinear differential equation of nanobeams under a concentrated load are obtained using the homotopy analysis method (HAM). Results are presented for nanobeams with clamped-free, simply supported, and clamped–clamped, boundary conditions. The obtained analytical solutions show good agreement with numerical methods reported in the literature. The effects of surface stresses on the bending behavior of silicon nanobeams are investigated using the developed solution method.