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# Two Dimensional Nonlocal Elasticity Analysis by Local Integral Equation Method

P.H. Wen1, X.J. Huang1, M.H. Aliabadi2
School of Engineering and Material Sciences, Queen Mary, University of London, London, UK, E1 4NS
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.

### Keywords

Two dimensional nonlocal elasticity, Eringen’s model, local integral equation method, weak form, radial basis functions.

Wen, P., Huang, X., Aliabadi, M. (2013). Two Dimensional Nonlocal Elasticity Analysis by Local Integral Equation Method. CMES-Computer Modeling in Engineering & Sciences, 96(3), 199–225.

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