Static analysis of functionally graded nanobeams based on Euler–Bernoulli and Timoshenko theories via complementary functions method

Alhasan A. M. W., NOORI A. R.

Mechanics Research Communications, cilt.150, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 150
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/j.mechrescom.2025.104571
  • Dergi Adı: Mechanics Research Communications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: Beam theories, Complementary functions method, Functionally graded nanobeams, Nonlocal elasticity, Static analysis
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

This study investigates the static behavior of functionally graded (FG) nanobeams. Formulations are carried out using the Euler–Bernoulli and Timoshenko beam theories framework. The canonical governing equations are derived for the first time and solved using the Complementary Functions Method (CFM). The transverse deflections for a range of material gradient indices, nonlocal parameters, slenderness ratios, and different boundary conditions are obtained. Benchmark comparisons validate the accuracy of the proposed model, and new numerical data are presented for cantilever and clamped-supported beams. Results confirm that increased nonlocality and gradation amplify deflections, especially in thick beams where shear effects are significant. The findings affirm the CFM's capability in accurately capturing scale-dependent mechanics, offering a reliable numerical platform for advanced nanoscale beam design.