A robust four-node quadrilateral element for laminated composite and sandwich plates based on Refined Zigzag Theory. (1st January 2021)

• Record Type: Journal Article
• Authors: Sorrenti, M.; Di Sciuva, M.; Tessler, A.
• Is Part Of: Computers & structures. Volume 242(2020)
• Publication Date: 2021-01-01
• Subjects: Refined Zigzag Theory -- Quadrilateral plate element -- Transverse shear locking -- Anisoparametric interpolation -- Multi-layered composite and sandwich plates; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2020.106369
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: A new locking-free finite-element based on Refined Zigzag Theory is proposed. Anisoparametric interpolation and a new element shear correction factor were used. Bending and free vibrational problems were studied for different composite plates. Very accurate results are obtained using this newly developed element. Abstract: The paper presents a locking-free four-node element for laminated composite and sandwich plates based on Refined Zigzag Theory (RZT). Initially, two RZT-based plate elements are derived using four-node and eight-node configurations, achieved by way of standard C 0 isoparametric shape functions. In addition, with a view on improving the modelling of extremely thin plates, an anisoparametric four-node element is developed in which the transverse deflection variable is interpolated using quadratic polynomial shape functions, whereas the remaining kinematic variables are bilinear. A straightforward transverse-shear edge-constraint procedure gives rise to a four-node anisoparametric element. A further enhancement is achieved using an Element Shear Correction (ESC) factor that is derived from a strain-energy matching procedure. The resulting four-node element (ZQ4c) uses full Gauss quadrature, consistent load vector, and mass matrix. Furthermore, the ZQ4c stiffness matrix has no spurious zero-energy modes, and the element is extremely robust when modelling ultra-thin plates. Several numerical studies are carried out to demonstrate the predictive capabilities of the four elements examined in this investigation. It is concluded ZQ4c is a highly accurate element over a wide range of material systems and span-to-thickness ratios, and is the best performing element of the four elements examined in this study.