# Robust Displacement and Mixed CUF-Based Four-Node and Eight-Node Quadrilateral Plate Elements

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## Abstract

This paper presents two classes of new four-node and eight-node quadrilateral finite elements for composite plates. Variable kinematics plate models are formulated in the framework of Carrera’s Unified Formulation, which encompass Equivalent Single Layer as well as Layer-Wise models, with the variables that are defined by polynomials up to 4th order along the thickness direction z. The two classes refer to two variational formulations that are employed to derive the finite elements matrices, namely the Principle of Virtual Displacement (PVD) and Reissner’s Mixed Variational Theorem (RMVT). For the PVD based elements, the main novelty consists in the extension of two field compatible approximations for the transverse shear strain field, referred to as QC4 and CL8 interpolations, which eliminate the shear locking pathology by constraining only the ɀ–constant transverse shear strain terms, to all variable kinematics plate elements. Moreover, for the first time the QC4 and CL8 interpolations are introduced for the transverse shear stress field within RMVT based elements. Preliminary numerical studies are proposed on homogeneous isotropic plates that demonstrate the absence of spurious modes and of locking problems as well as the enhanced robustness with respect to distorted element shapes. The new QC4 and CL8 variable kinematics plate elements display excellent convergence rates and yield accurate responses for both, thick and thin plates.

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