A novel mixed finite element formulation based on the refined zigzag theory for the stress analysis of laminated composite plates

This study presents an accurate mixed variational formulation for the stress analysis of laminated composite plates based on Refined Zigzag Theory (RZT). A two-field variational concept based on the Hellinger-Reissner (HR) principle is employed associated with the kinematic assumptions of the RZT. The RZT provides a good mixture between the accuracy and computational efficiency for the thin and thick laminated composite structures without using the shear correction factors. A four-noded quadrilateral element and bi-linear shape functions are used for the discretization of the solution domain ensuring the C⁰-continuity. The main novelty of the present study is that the flexural behavior of the laminated composite plates is investigated based on RZT within the light of HR principle using monolithic approach for the first time. The proposed Mixed Finite Element (MFE) formulation assigns stress resultant type field variables in addition to the kinematic variables of the RZT. Therefore, the present approach, MRZT, paves the way of obtaining the stress resultants at each node directly from the solution of the system equations. Since the shear forces are obtained at each node, Equivalent (transformed) Section Principle (ESP) is utilized to achieve continuous through thickness transverse shear stress variations. In-plane strain components are calculated through the compliance matrix without resorting to the spatial derivatives of displacement components. The robustness and capability of the present approach are established through benchmark problems, and its applicability to challenging problems is demonstrated by modeling thick and highly heterogeneous plates, a delaminated plate and three-point bending tests.