No abstract

The present research focuses on the use of a meshless method for the solution of nanoplates by considering strain gradient thin plate theory. Unlike the most common finite element method, meshless methods do not rely on a domain decomposition. In the present approach approximating functions at collocation nodes are obtained by using radial basis functions which depend on shape parameters. The selection of such parameters can strongly influences the accuracy of the numerical technique. Therefore the authors are presenting some numerical benchmarks which involve the solution of nanoplates by employing an optimization approach for the evaluation of the undetermined shape parameters. Stability is discussed as well as numerical reliability against solutions taken for the existing literature.

No abstract

No abstract

This paper presents the static bending of isotropic Kirchhoff’s nanoplates modelled using the second-order strain gradient theory. The numerical analysis is conducted using mesh free methods instead of traditional finite elements. To the best of the authors’ knowledge, no such meshless methods have been employed in the analysis of strain gradient nanoplates. Hermite radial point interpolation method is used to approximate the bending degrees of freedom. Plates with different geometries and simply supported boundary conditions are studied. The results are then compared with the analytical solution available in the literature.