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Airy Stress Functions for Transverse Sinusoidally Loaded Beam in Nonlocal Elasticity

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On the face of difficulty of employing the nonlocal constitutive relations in the form of integral equation, researchers started to seek alternative forms of the nonlocal constitutive relations. The Greens function formalism has become the most popular one for this purpose. The nonlocal constitutive equation in differential equation form allows employing stress potentials, such as Airys stress functions to solve boundary value problems in nonlocal elasticity. For the nonlocality kernel of exponential form, the differential equation for Airy's functions in nonlocal elasticity can be obtained by introducing the strains into the compatibility condition. In this work Airy's stress functions for plane stress problems in nonlocal elasticity are studied. Appropriate function forms for the Airys stress function are considered and are applied to solve transversely sinusoidal loaded cantilever beam bending problems. The solutions are compared with their classical counterparts. The results are given in a series of figures and tables. The results indicate that the influence of nonlocal effect becomes stronger as the wave length of sinusoidal loading come near to the length of beam which can not comment by experiments and nonlocal elasticity has more potential to represent the mechanical behavior of nanostructures and nonlocal effects could be significant in nanotechnology.
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Document Type: Research Article

Publication date: October 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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