Nonlocal elasticity theory for bending and free vibration analysis of nano plates

비국소 탄성 이론을 이용한 나노 판의 휨 및 자유진동해석

  • Lee, Won-Hong (Department of Civil Engineering, Gyeongnam National University of Science and Technology) ;
  • Han, Sung-Cheon (Department of Civil & Railroad Engineering, Daewon University College) ;
  • Park, Weon-Tae (Division of Construction and Environmental Engineering, Kongju National University)
  • 이원홍 (경남과학기술대학교 토목공학과) ;
  • 한성천 (대원대학교 철도건설과) ;
  • 박원태 (공주대학교 건설환경공학부)
  • Received : 2012.05.08
  • Accepted : 2012.07.12
  • Published : 2012.07.31


In this paper, we study the bending and free vibration analysis of nano plate, using a nonlocal elasticity theory of Eringen with a third-order shear deformation theory. This theory has ability to capture the both small scale effects and quadratic variation of shear strain and consequently shear stress through the plate thickness. Analytical solutions of bending and vibration of a laminated composite nano plate are presented using this theory to illustrate the effect of nonlocal theory on deflection of the nano plates. The relations between nonlocal third-order and local theories are discussed by numerical results. Further, effects of (i) nonlocal parameters, (ii) laminate schemes, (iii) directions of the fiber angle and (iv) number of layers on nondimensional deflections are investigated. In order to validate the present solutions, the reference solutions are used and discussed. The results of anisotropic nano plates using the nonlocal theory may be the benchmark test for the bending analysis.


Nonlocal elasticity theory;Third-order shear deformation theory;Bending analysis;Free vibration analysis;Nano plates


Supported by : 경남과학기술대학교


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