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ARTICLE

Two Dimensional Nonlocal Elasticity Analysis by Local Integral Equation Method

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1 School of Engineering and Material Sciences, Queen Mary, University of London, London, UK, E1 4NS
2 Department of Aeronautics, Imperial College, London, UK, SW7 2BY

Computer Modeling in Engineering & Sciences 2013, 96(3), 199-225. https://doi.org/10.3970/cmes.2013.096.199

Abstract

In this paper, a Local Integral Equation Method (LIEM) is presented for solving two-dimensional nonlocal elasticity problems . The approach is based on the Eringen’s model with LIEM and the interpolation using the radial basis functions to obtain the numerical solutions for 2D problems. A weak form for the set of governing equations with a unit test function is transformed into the local integral equations. The meshless approximation technique with radial basis functions is employed for the implementation of displacements. A set of the local domain integrals is obtained in analytical form for the local elasticity and by using a standard integral scheme for the nonlocal elasticity. Three examples are presented to demonstrate the convergence and accuracy of LIEM including a rectangular plate, disk and a plate containing a circular hole subjected to a uniformly distributed displacement or tensile load. Comparisons have been made with the solutions of one dimension problems and other numerical techniques including the finite integration method, the finite/boundary element methods.

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