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Nonlocal elasticity in plates using novel trial functions / Sh. Faroughi; S.M.H. Goushegir; H. Haddad Khodaparast; M.I. Friswell; Michael Friswell; Hamed Haddad Khodaparast
International Journal of Mechanical Sciences, Volume: 130, Pages: 221 - 233
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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...
|Published in:||International Journal of Mechanical Sciences|
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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
College of Engineering