3rd International Conference on Mechanics of Composites, Bologna, Italy, 4 - 07 July 2017
Another alternative to 3-D finite element model is the use of plate elements based on a single-layer plate theory with zigzag functions, referred to as Refined Zigzag Theory (RZT). This study presents a new three-node flat shell element based on RZT. The element has 11 degrees of freedom (dof) at the corner nodes. Also, it is available as an ABAQUS user element.
It accounts for both transverse stretching and transverse shear deformations in laminated composite structures. The representation of kinematic variables includes quadratic shape functions for the in-plane and transverse displacements, and linear shape functions for the average rotations and the zigzag amplitudes. The zigzag kinematics represented by piecewise-linear C0-continuous functions through the thickness enable sufficiently accurate and computationally efficient modeling of a wide range of homogeneous and heterogeneous laminates without the use of shear correction factors.
The consequence of the kinematic assumptions leads to an element with three corner nodes and three mid-side nodes. The corner nodes have nine dof consisting of in-plane displacements, out-of-plane slopes, transverse displacement, and its symmetric and anti-symmetric modes, out-of-plane zigzag rotations. The mid-side nodes have only the transverse displacement as a dof. After introducing the mathematical drilling rotation and drilling zigzag dof at the corner nodes, the mid-side dof is removed by enforcing continuous shear strain constraints along the three element edges.
The stress resultants obtained from the equilibrium equations are physically consistent with their definitions based on Hooke’s relations. Therefore, the stress fields can be directly calculated from the strain fields. However, the accuracy of the transverse stress components is enhanced by integration through the thickness in conjunction with peridynamic differentiation. This element provides a robust and accurate prediction of all stress components in highly heterogeneous laminates. Its accuracy is demonstrated by considering a simply supported sandwich panel made of a soft core with graphite/epoxy face sheets under transverse sinusoidal load. The comparison of the results from this element and the analytical solution shows close agreement.