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Airy's Functions in Nonlocal Elasticity

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Nanostructured devices and materials, such as carbon nanotubes, Atomic Force Microscope, MEMS, etc. attract increasing attention in the scientific world. It has been realized that the classical elasticity is not capable to capture the mechanical behavior of them precisely. There is a wide consensus among the scientists that nonlocal elasticity is more capable than the classical counterpart to model the mechanical behavior of nanostructured materials and devices. In this paper a method which is useful for solving problems in nonlocal is introduced. Airy's stress functions for plane stress problems in nonlocal elasticity are studied. The nonlocal constitutive equations in integral form are discussed and a method is suggested to invert the constitutive equation which allows expressing strains in terms of stresses. A qualitative discussion is given on this inversion process. For the nonlocality kernel of exponential form, the differential equation for Airy's functions in nonlocal elasticity is obtained by introducing the strains into the compatibility condition. Appropriate polynomial forms for the Airy's function are considered and are applied to solve beam bending problems. The solutions are compared with their classical counterparts. The results are given in a series of figures and tables and are discussed in detail. This paper is concluded by indicating the implications of the presented study in nanomechanics and nanotechnology.
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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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