Abstract
The present work focuses on the formulation and numerical assessment of a family of C0 quadrilateral plate elements based on the refined zigzag theory (RZT). Specifically, four quadrilateral plate elements are developed and numerically tested: The classical bi-linear 4-node element (RZT4), the serendipity 8-node element (RZT8), the virgin 8-node element (RZT8v), and the 4-node anisoparametric constrained element (RZT4c). To assess the relative merits and drawbacks, numerical tests on bending (maximum deflection and stresses) and free vibration analysis of laminated composite and sandwich plates under different boundary conditions and transverse load distributions are performed. Convergences studies with regular and distorted meshes, transverse shear-locking effect for thin and very thin plates are carried out. It is concluded that the bi-linear 4-node element (RZT4) has performances comparable to the other elements in the range of thin plates when reduced integration is adopted but presents extra zero strain energy modes. The serendipity 8-node element (RZT8), the virgin 8-node element (RZT8v), and the 4-node anisoparametric constrained element (RZT4c) show remarkable performance and predictive capabilities for various problems, and transverse shear-locking is greatly relieved, at least for aspect ratio equal to 5 × 102, without using any reduced integration scheme. Moreover, RZT4c has well-conditioned element stiffness matrix, contrary to RZT4 using reduced integration strategy, and has the same computational cost of the RZT4 element.
Highlights
In the last decades, multi-layered composite and sandwich structures have been increasingly used in different engineering fields, thanks to their advantages over the traditional metallic structures due to their high specific stiffness and strength and their tailoring capabilities
Contrary to the classical plate theory (CPT), the first-order shear deformation theory (FSDT), first formulated by Mindlin and extended to the heterogeneous anisotropic plates by Whitney and Pagano [3], allows the rotation of the normal to the reference surface to be independent of the slope of the reference surface
C0-continous elements are the most-widely used in commercial finite element software due to their computational efficiency, it is well known that overstiff unrealistic numerical results are obtained when using the conventional low-order isoparametric C0 finite elements in the analysis of thin and very thin plates; this phenomenon is known in the literature as the transverse shear-locking effect, according to Oñate [38,39,40]
Summary
Multi-layered composite and sandwich structures have been increasingly used in different engineering fields (aerospace, automotive, marine, nuclear, and civil), thanks to their advantages over the traditional metallic structures due to their high specific stiffness and strength and their tailoring capabilities. In order to simulate the distortion of the normal and the step-wise distribution of the transverse shear stresses along the thickness typical of multi-layered structures, in the ZZT the in-plane displacements are written as a superposition of a through-the-thickness polynomial distribution (global contribution such as in the ESL theories) and a piecewise linear continuous function, (local or zigzag contribution). The discrete penalty constraints, such as the discrete Kirchhoff theory (DKT) [47,48], where the transverse shear strain energy is neglected in the formulation and the Kirchhoff assumption of zero transverse shear strains are imposed at specific discrete points in the element are commonly used; the mixed interpolation of tensorial components (MITC) strategy [49,50], in which ad hoc chosen strain fields are tied to the displacement-based strains; B-bar method [51]; and F-bar method [52,53], which relies on the concept of deviatoric/volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart. We use the subscript b and t to indicate the top and bottom surfaces of the plate
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
