Thèse de Thi Huyen Cham LE
Robust variables kinematics plate finite elements for composite structures
soutenue le 26 juin 2019

Abstract. Composite structures are used progressively in the engineering applications. The main advantages of composite materials are their high strength and sti ness with a low density allowing for weight reduction in the structures. Composite structures are made of several layers of different materials which are perfectly bonded together. In the field of geometrical approximations, a plate or shell model can be employed when the thickness is signiffcantly smaller than other two dimensions. An overview of classical and reffined plate models in the open literature is described in the first part of this thesis. The aim of this work is the development of 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 (CUF), which encompasses Equivalent Single Layer (ESL) as well as Layer-Wise (LW) models, with the variables that are defined by polynomials up to 4th order along the thickness direction z. The primary variables with an ESL description are described along the thickness of all layers of the laminate, while LW descriptions employ polynomials for each layer independently. 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). PVD is known as a purely displacement-based models, while RMVT allows to introduce independent assumptions for the transverse stress and the displacement fields. Thanks to the static condensation technique, a Hybrid formulation based on the RMVT is derived. A detailed description of CUF-based plate models is reported in the second part of this thesis. The main advantage of CUF is to permit to implement a series of variable kinematics models within a single program. For the purpose of eliminating the shear locking pathology, two field compatible approximations for only the z-constant transverse shear strain terms, referred to as QC4 and CL8 interpolations, are extended to all variable kinematics CUF plate elements. Moreover, the QC4S and CL8S interpolations, are also introduced for the transverse shear stress field within RMVT-based and Hybrid mixed-based elements.
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. Present results are compared against solutions obtained with several isoparametrical approaches. The present variable kinematics plate elements display excellent convergence rates under different boundary and loading conditions and yield accurate responses for both, thick and thin plates. In addition, several numerical investisgations for some mechanical problem for laminated composite plates, such as Pagano's plate and plate with a circular hole benchmarks, are then presented. Numerical results in comparison with those available in literature show that the proposed FEs are efficient for modeling a robust finite elements.

Mis à jour le 20 septembre 2019