Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory

AKGÖZ B., CİVALEK Ö.

ARCHIVE OF APPLIED MECHANICS, cilt.82, sa.3, ss.423-443, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 82 Sayı: 3
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1007/s00419-011-0565-5
  • Dergi Adı: ARCHIVE OF APPLIED MECHANICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.423-443
  • Anahtar Kelimeler: Strain gradient elasticity, Micro beams, Static analysis, Size effect, Modified couple stress, Bernoulli-Euler beam, Poisson's ratio, COUPLE STRESS THEORY, DEFORMABLE SHELL-MODEL, DYNAMIC-ANALYSIS, STATIC DEFLECTION, FREE-VIBRATION, MICROTUBULES, PLATES, EQUILIBRIUM, STABILITY
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Bending analysis of micro-sized beams based on the Bernoulli-Euler beam theory is presented within the modified strain gradient elasticity and modified couple stress theories. The governing equations and the related boundary conditions are derived from the variational principles. These equations are solved analytically for deflection, bending, and rotation responses of micro-sized beams. Propped cantilever, both ends clamped, both ends simply supported, and cantilever cases are taken into consideration as boundary conditions. The influence of size effect and additional material parameters on the static response of micro-sized beams in bending is examined. The effect of Poisson's ratio is also investigated in detail. It is concluded from the results that the bending values obtained by these higher-order elasticity theories have a significant difference with those calculated by the classical elasticity theory.