C0 triangular elements based on the Refined Zigzag Theory for multilayer composite and sandwich plates

Abstract The Refined Zigzag Theory (RZT) has been recently developed for the analysis of homogeneous, multilayer composite and sandwich plates. The theory has a number of practical and theoretical advantages over the widely used First-order Shear Deformation Theory (FSDT) and other types of higher-order and zigzag theories. Using FSDT as a baseline, RZT takes into account the stretching, bending, and transverse shear deformations. Unlike FSDT, this novel theory does not require shear correction factors to yield accurate results for a wide range of material systems including homogeneous, laminated composite, and sandwich laminates. The inplane zigzag kinematic assumptions, which compared to FSDT add two additional rotation-type kinematic variables, give rise to two types of transverse shear strain measures – the classical average shear strain (as in FSDT) and another one related to the cross-sectional distortions enabled by the zigzag kinematic terms. Consequently, with a fixed number of kinematic variables, the theory enables a highly accurate modeling of multilayer composite and sandwich plates even when the laminate stacking sequence exhibits a high degree of transverse heterogeneity. Unlike most zigzag formulations, this theory is not affected by such theoretical anomalies as the vanishing of transverse shear stresses and forces along clamped boundaries. In this paper, six- and three-node, C 0 -continuous, RZT-based triangular plate finite elements are developed; they provide the best compromise between computational efficiency and accuracy. The element shape functions are based on anisoparametric (aka interdependent) interpolations that ensure proper element behavior even when very thin plates are modeled. Continuous edge constraints are imposed on the transverse shear strain measures to derive coupled-field deflection shape functions, resulting in a simple and efficient three-node element. The elements are implemented in ABAQUS – a widely used commercial finite element code – by way of a user-element subroutine. The predictive capabilities of the new elements are assessed on several elasto-static problems, which include simply supported and cantilevered laminated composite and sandwich plates. The numerical results demonstrate that the new RZT-based elements provide superior predictions for modeling a wide range of laminates including highly heterogeneous sandwich laminations. They also offer substantial improvements over the existing plate elements based on FSDT as well as other higher-order and zigzag-type elements.

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