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http://dx.doi.org/10.12989/anr.2022.12.1.037

Eringen's nonlocal theory for non-linear bending analysis of BGF Timoshenko nanobeams  

Azandariani, Mojtaba Gorji (Structural Engineering Division, Faculty of Civil Engineering, Semnan University)
Gholami, Mohammad (Department of Civil Engineering, Yasouj University)
Nikzad, Akbar (Department of Civil Engineering, Islamic Azad University of Bushehr)
Publication Information
Advances in nano research / v.12, no.1, 2022 , pp. 37-47 More about this Journal
Abstract
In this paper, the non-linear static analysis of Timoshenko nanobeams consisting of bi-directional functionally graded material (BFGM) with immovable ends is investigated. The scratching in the FG nanobeam mid-plane, is the source of nonlinearity of the bending problems. The nonlocal theory is used to investigate the non-linear static deflection of nanobeam. In order to simplify the formulation, the problem formulas is derived according to the physical middle surface. The Hamilton principle is employed to determine governing partial differential equations as well as boundary conditions. Moreover, the differential quadrature method (DQM) and direct iterative method are applied to solve governing equations. Present results for non-linear static deflection were compared with previously published results in order to validate the present formulation. The impacts of the nonlocal factors, beam length and material property gradient on the non-linear static deflection of BFG nanobeams are investigated. It is observed that these parameters are vital in the value of the non-linear static deflection of the BFG nanobeam.
Keywords
Eringen's nonlocal theory; bi-directional functionally graded; nanobeam; non-linear static deflection; Timoshenko theory;
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