On the mapping procedure based on higher‐order Hermite polynomials for laminated thin plates with arbitrary domains in gradient elasticity

Abstract

The article presents a finite element mapping procedure for the coordinate change via higher-order derivatives to compute the fundamental matrices of laminated thin plates with arbitrary domains in gradient elasticity. In this context, the approximate solution requires Hermite interpolating functions.Therefore, conforming and nonconforming formulations are needed for both membrane and bending degrees of freedom, which require respectively C 1 and C 2 continuity. The aim of the current procedure is the possibility to remove the limitations related to the regular rectangular shape which typically characterizes this kind of elements and to introduce arbitrary distortions, discussing the influence of structured and unstructured meshes. The accuracy and convergence features of the methodology are presented through some numerical tests and compared to relevant literature.