Optimization of a Radial Point Interpolation Meshless strategy for strain gradient nanoplates

Abstract

A parameter optimization of the Radial Point Interpolation Meshless Method (RPIM) is presented in this work for solving the static bending analysis of Kirchhoff nanoplates which include the first order strain gradient theory. Optimization in meshless strategies is often required since shape parameters, of the Radial Basis Functions (RBFs) used, strongly influence the numerical results when different geometries, boundary conditions or various mechanical aspects are considered. Due to the introduction of a first order strain gradient theory within Kirchhoff plate framework, to approximate the bending degrees of freedom, a Hermite RPIM is used. The static deflection of thin plates with different aspect ratios and boundary conditions is analysed. The results of the static analysis are compared with the solutions available in the literature and good agreement among all presented results as well as convergence behaviour is shown.