Conforming and nonconforming laminated finite element Kirchhoff nanoplates in bending using strain gradient theory

This paper presents a comprehensive numerical finite element implementation of the nonlocal strain gradient theory applied to thin laminated composite nanoplates using Kirchhoff theory (known as Classical Laminated Plate Theory or CLPT). Hermite interpolation functions are used to approximate membrane and bending degrees of freedom according to the conforming and nonconforming approaches. To the best of the authors’ knowledge, there is no finite element formulation in the literature able to deal with laminated Kirchhoff plates including the strain gradient theory, which allows to consider general stacking sequences and boundary conditions. A simple and effective matrix notation is employed to facilitate the computer implementation. Benchmarks reported prove the accuracy of the implementation. Novel applications are provided for further developments in the subject.