### Nonlocal elasticity in plates using novel trial functions

International Journal of Mechanical Sciences, Volume: 130, Pages: 221 - 233

Swansea University Authors:

• PDF | Accepted Manuscript

DOI (Published version): 10.1016/j.ijmecsci.2017.05.034

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 computat...

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Published in: International Journal of Mechanical Sciences 00207403 2017 https://cronfa.swan.ac.uk/Record/cronfa34213 No Tags, Be the first to tag this record!
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. Two-phase integro-differential formulation; Ritz Method; Boundary characteristic orthogonal polynomials; Kirchhoff plate; Static deflection; Dynamic analysis Faculty of Science and Engineering 221 233