Nonlocal Elasticity in Plates using Novel Trial Functions

S Faroughi, SMH Goushegir (Urmia University of Technology, Iran), H Haddad Khodaparast & MI Friswell (Swansea University)

International Journal of Mechanical Sciences, Vol. 130, September 2017, pp. 221-233

Abstract

This study presents the Ritz formulation, which is based on boundary characteristic orthogonal polynomials (BCOPs), for the two-phase integro-differential form of the Eringen nonlocal elasticity model. This approach is named the nonlocal Ritz method (NL-RM). This feature greatly reduces the computational cost compared to the nonlocal finite-element method (NL-FEM). Another advantage of this approach is that, unlike NL-FEM, the nonlocal mass and stiffness matrices are independent of the mesh distribution. Here, these formulations are applied to study the static-bending and free-dynamic analyses of the Kirchhoff plate model. In this paper, novel 2D BCOPs of the plate are derived as coordinate functions. These polynomials are generated using a modified Gram-Schmidt process and satisfy the given geometrical boundary conditions as well as the natural boundary conditions. The accuracy and convergence of the presented model, demonstrated through several numerical examples, are discussed. A concise argument on the advantages of NL-RM compared to NL-FEM is also provided.

Paper Availability

This material has been published in the International Journal of Mechanical Sciences, Vol. 130, September 2017, pp. 221-233, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier.


Link to paper using doi: 10.1016/j.ijmecsci.2017.05.034

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