Finite element models with node-dependent kinematics adopting Legendre polynomial expansions for the analysis of laminated plates

This work presents a new class of advanced plate FEM models with node-dependent kinematics. To capture the high local stress gradients in the analysis of composite structures, refined models are essential; while for the rest region of the structure, usually, low-order models can be sufficient. An innovative approach named as node-dependent kinematics is proposed to integrate models with different levels of refinement to reach an optimal balance between accuracy and solution costs in FEM analysis. Node-dependent kinematics is based on Carrera Unified Formulation (CUF), which introduces thickness functions defined on the thickness domain for the refinement of plate models. Both ESL (Equivalent Single Layer) and LW (Layer-wise) models adopting various approximation theories can be described and implemented in such a framework. CUF-type displacement functions allow the thickness functions to be related to specific FEM nodes before the interpolation of them over the in-plane domain of the element, leading to advanced FEM models with node-dependent kinematics. In this way, a kinematic variation can be conveniently obtained, which can bridge a global model to a locally refined model while keeping the displacement continuity. Hierarchical Legendre Expansions (HLE) are adopted to construct the shape functions in this work, which provides an approach to capture the localized effects without re- meshing on the structure. Governing equations for FEM models with node-dependent kinematics are derived from the Principle of Virtual Displacements (PVD). When used in the analysis of laminated plates with local effects to be accounted for, the proposed advanced plate models can reduce the computational costs greatly while guaranteeing accuracy without employing special global-local coupling methods.