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Weak Formulation of Finite Element Method for Nonlocal Beams Using Additional Boundary Conditions

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The finite element method for the Euler-Bernoulli beam model is applied for the bending analyzes of micro/nanobeams with the additional boundary conditions. Nonlocal stiffness matrix and force vector is calculated to solve beam bending problems. A qualitative discussion is given on this calculation process. The study contains two major parts, namely, finite element modeling of nonlocal beams with the additional boundary conditions and nonlocal theory based approach for predicting behavior of Carbon Nanotubes (CNTs). The nonlocal solutions are compared with their classical counterparts. The results illustrate that the deflection and bending moment of nonlocal beam depend on the small scale parameters and also on the boundary condition of the beam and the applied load.
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Keywords: ADDITIONAL BOUNDARY CONDITIONS; CARBON NANOTUBE; FINITE ELEMENT METHOD

Document Type: Research Article

Publication date: November 1, 2011

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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