Bending of small-scale Timoshenko beams based on the integral/differential nonlocal-micropolar elasticity theory: a finite element approach

  • M. Faraji-Oskouie
  • A. Norouzzadeh
  • R. AnsariEmail author
  • H. Rouhi


A novel size-dependent model is developed herein to study the bending behavior of beam-type micro/nano-structures considering combined effects of nonlocality and micro-rotational degrees of freedom. To accomplish this aim, the micropolar theory is combined with the nonlocal elasticity. To consider the nonlocality, both integral (original) and differential formulations of Eringen's nonlocal theory are considered. The beams are considered to be Timoshenko-type, and the governing equations are derived in the variational form through Hamilton's principle. The relations are written in an appropriate matrix-vector representation that can be readily utilized in numerical approaches. A finite element (FE) approach is also proposed for the solution procedure. Parametric studies are conducted to show the simultaneous nonlocal and micropolar effects on the bending response of small-scale beams under different boundary conditions.

Key words

integral model of nonlocal elasticity differential model of nonlocal elasticity micropolar theory finite element (FE) analysis Timoshenko nano-beam 

Chinese Library Classification

O346 O242.21 

2010 Mathematics Subject Classification

82D80 74K10 65N30 82B31 


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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • M. Faraji-Oskouie
    • 1
  • A. Norouzzadeh
    • 1
  • R. Ansari
    • 1
    Email author
  • H. Rouhi
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of GuilanRashtIran
  2. 2.Department of Engineering ScienceFaculty of Technology and Engineering, University of GuilanRudsar-VajargahIran

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