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# Line element-less method (LEM) for arbitrarily shaped nonlocal nanoplates: exact and approximate analytical solutions

## Line element-less method (LEM) for arbitrarily shaped nonlocal nanoplates: exact and approximate analytical solutions

### Alberto DI MATTEO, Antonina PIRROTTA

Abstract. This paper presents an innovative procedure for the analysis of nonlocal plates with arbitrary shape and various boundary conditions. In this regard, the Eringen’s nonlocal model is used to capture small length scale effects. The proposed procedure, referred to as Line Element-Less Method (LEM), is a completely meshfree approach requiring the evaluations of simple line integrals along the plate boundary parametric equation. Further, the deflection function is represented by a series expansion is terms of harmonic polynomials whose coefficients are found by performing variations of appropriately introduced functionals, leading to a linear system of algebraic. Notably, the proposed procedure yields approximate analytical solutions for general shapes and boundary conditions, and even exact solutions for some plate geometries.

Keywords
Kirchoff Plate, Nonlocal Eringen Model, Harmonic Polynomials, Line Element-Less Method, Meshfree Method

Published online 3/17/2022, 6 pages

Citation: Alberto DI MATTEO, Antonina PIRROTTA, Line element-less method (LEM) for arbitrarily shaped nonlocal nanoplates: exact and approximate analytical solutions, Materials Research Proceedings, Vol. 26, pp 613-618, 2023

DOI: https://doi.org/10.21741/9781644902431-99

The article was published as article 99 of the book Theoretical and Applied Mechanics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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