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Steel and Composite Structures
  Volume 32, Number 3, August10 2019 , pages 293-304
DOI: https://doi.org/10.12989/scs.2019.32.3.293
 


Nonlocal geometrically nonlinear dynamic analysis of nanobeam using a meshless method
Mohammad Hossein Ghadiri Rad, Farzad Shahabian and Seyed Mahmoud Hosseini

 
Abstract
    In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.
 
Key Words
    cnonlocal elasticity; element-free Galerkin (EFG) method; dynamic analysis; total Lagrangian approach; geometrically nonlinear analysis
 
Address
(1) Mohammad Hossein Ghadiri Rad:
Civil Engineering Department, Quchan University of Technology, Quchan, Iran;
(2) Farzad Shahabian:
Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran;
(3) Seyed Mahmoud Hosseini
Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.
 

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