Zigzag Theory Applications in Composite Plate Structures

Zigzag theories represent a class of higher-order plate models developed to bridge the gap between computationally expensive three-dimensional elasticity solutions and overly simplistic single-layer approximations. By superimposing a global displacement field with local, piecewise functions across the laminate thickness, these theories capture the characteristic “zigzag” variation of in-plane displacements and enforce continuity of transverse shear stresses at ply interfaces. As a result, they provide accurate predictions of bending, vibration and buckling behaviour in thick or highly heterogeneous composite plates, where classical shear deformation theories tend to underpredict transverse deflections and overpredict interlaminar stresses. Recent advances have refined the kinematic assumptions—ranging from cubic and parabolic through-thickness expansions to mixed variational formulations—while numerical implementations have been embedded in efficient finite-element schemes. Global analyses of overall stiffness and local assessments of stress concentrations can thus be performed within a unified framework, enabling reliable design and optimisation of modern composite structures in aerospace, civil engineering and marine applications.

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Zigzag Theory Applications in Composite Plate Structures publication trend

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Technical terms

Zigzag Theory: A layer-wise plate modelling approach that superposes a global polynomial displacement field with local piecewise functions to represent the alternating slope of in-plane displacements across ply interfaces.

Refined Zigzag Theory (RZT): An advanced zigzag formulation that employs higher-order kinematic functions—typically cubic for in-plane and parabolic for transverse displacements—to improve the fidelity of stress and displacement predictions.

Equivalent Single-Layer (ESL) Model: A homogenised plate theory that treats a multilayer laminate as a single continuum endowed with enriched kinematics to account for transverse shear and zigzag effects.

Transverse Shear Deformation: Shearing strains acting perpendicular to the plate mid-plane, critical for accurate analysis of thick or highly orthotropic laminates.

Hellinger–Reissner Principle: A mixed variational formulation in which displacements and stresses are treated as independent fields, ensuring interlaminar equilibrium and compatibility through a single energy functional.

References

1. New Accomplishments on the Equivalence of the First-Order Displacement-Based Zigzag Theories through a Unified Formulation. Journal of Composites Science (2024).
2. A new mixed model based on the enhanced-Refined Zigzag Theory for the analysis of thick multilayered composite plates. Composite Structures (2023).
3. An edge-based smoothed three-node composite plate element with refined zigzag kinematics. Composite Structures (2021).