PSI - Issue 70

Aamir Anwar Nezami et al. / Procedia Structural Integrity 70 (2025) 105–112

106

1. Introduction

Laminated composite plates have become very important in modern engineering applications due to their high strength-to-weight ratio and highly customizable mechanical properties. These structures are constructed by stacking multiple layers of thin laminae (made of materials such as glass, carbon, or aramid fibres), which are bonded with polymer-based adhesives to achieve desired structural characteristics. This wide adaptable design features makes laminated composites particularly valuable in aerospace, automotive, marine, and civil engineering structures. Analysing the mechanical behaviour of laminated composite plates requires accurate prediction of deformation patterns, stress distributions, and potential failure mechanisms to ensure structural integrity and optimizing design. One of the critical aspect of laminated composites is it's proneness to interlaminar weaknesses due to use of polymer adhesives, which often possess lower strength compared to the fibre-reinforced plies. These weaknesses can lead to delamination, transverse cracking, and reduced overall performance. Therefore, precise analysis of interlaminar strains and stresses is essential for predicting failure modes in thick laminated composite and sandwich plates. The presence of significant shear deformation and material discontinuities at layer interfaces leads to the well-known zigzag effect, characterized by abrupt slope changes through the plate's thickness Abrate and Di Scuiva (2017). This warping effect in laminated composite and sandwich plates was shown in the exact three-dimensional elasticity solutions proposed by Pagano (1970a). In exact three-dimensional elasticity theory, the unknown field variables are layer-dependent, causing computational costs to rise with an increasing number of laminae. To get rid of these issues, various ESL theories have been developed, including the CLPT, FSDT, and TSDT. However, these models often fail to accurately capture the warping of in-plane displacements, particularly in thick laminated composite and sandwich plates. The Zigzag theory represents much advancement in ESL approaches, effectively capturing the warping of in plane displacements while ensuring continuity of transverse shear stresses at layer interfaces through specialized zigzag continuity functions Di Scuiva (1992). The RZT, introduced by Tessler et al. (2009), enhanced upon earlier zigzag models by accurately modelling clamped boundary conditions. In RZT, the zigzag functions cannot predict the coupling effect of inplane displacements for anisotropic multilayered plates, such as angle-ply laminates. Sorrenti and Di Scuiva (2021) proposed Enhanced-RZT which considers coupling effects for an angle-ply laminates. Sorrenti and Gherlone (2023) recently extended Enhanced-RZT to incorporate cubic zigzag functions for improved accuracy. Si et al. (2023) also formulated a cubic higher-order zigzag theory, enhancing predictive capabilities but with increased computational costs. In addition to static and dynamic analysis, laminated composite plates are prone to buckling instability under compressive loads, which necessitates accurate prediction methods. Notable studies by Srinivas and Rao (1970), Jiarang and Jianqiao (1993), and Reddy and Phan (1985) have extensively investigated the buckling behaviour of laminated composite and sandwich plates. In this study, a higher-order zigzag theory is developed that is independent of the number of laminae, consisting only five unknowns. Inspired by elasticity solutions, this zigzag model effectively captures transverse shear stress continuity at layer interfaces. The resulting transverse shear strain varies quadratically through the thickness, accounting for discontinuities at layer interfaces. The proposed zigzag model is validated against various ESL theories (such as CLPT, FSDT, and TSDT), MZT, Enhanced-RZT, and Exact Three-Dimensional Elasticity solutions. Numerical investigations cover various stacking sequences, including cross-ply and angle-ply configurations, with additional attention given to buckling behaviour under compressive loading.

Nomenclature CLPT Classical Laminated Plate Theory FSDT First Order Shear Deformation Theory TSDT Third Order Shear Deformation Theory ESL Equivalent Single Layer RZT Refined Zigzag Theory MZT Murakami Zigzag Theory

2. Kinematics for Present zigzag structural plate theories Inspired by the elasticity solutions, this model effectively captures transverse shear stress continuity at layer interfaces. The resulting transverse shear strain varies quadratically through the thickness, accounting for discontinuities at layer interfaces as shown below in Equation (1).