Shear Deformation Theory in Composite Plate Analysis
Summary
Composite plates, including laminates and sandwich structures, derive their mechanical performance from the interaction of stiff reinforcement and ductile matrix through the thickness. Classical plate theory assumes that normals to the mid-plane remain straight and perpendicular after deformation, neglecting transverse shear strains and therefore losing accuracy in thick or layered configurations. Shear deformation theories extend the classical framework by introducing transverse shear effects explicitly into the displacement field. First-order shear deformation theory (FSDT) incorporates a constant shear strain through the thickness, requiring a shear correction factor to match three-dimensional elasticity. In contrast, higher-order shear deformation theories (HSDTs) and layerwise formulations employ polynomial, trigonometric, exponential or hyperbolic functions to represent realistic transverse shear and normal strain distributions, satisfying traction-free boundary conditions without empirical factors. Advances such as zigzag kinematics introduce piecewise variation of in-plane displacements, enabling accurate prediction of interlaminar stresses and enhancing computational efficiency. These formulations underpin finite element models and analytical solutions used in the bending, vibration and buckling analyses of composite and functionally graded plates, ensuring reliable design of lightweight structures across aerospace, automotive and civil engineering applications.
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Shear Deformation Theory in Composite Plate Analysis publication trend
The graph below shows the total number of articles in shear deformation theory in composite plate analysis across all publications each year (not limited to Nature Index journals).
Technical terms
Transverse shear deformation: deformation resulting from shear strains acting parallel to plate surfaces, significant in thick or layered plates.
Shear correction factor: empirical multiplier in first-order theories to adjust for non-uniform shear strain distribution through a plate’s thickness.
Higher-order shear deformation theory (HSDT): refined plate theory incorporating higher-order variations of displacement through thickness to satisfy zero shear stress at surfaces without empirical factors.
Zigzag kinematics: layerwise displacement model allowing slope discontinuities between laminae to capture interlaminar shear variation and improve stress predictions.
Navier solution: analytical technique using double trigonometric series for bending and vibration analysis of simply supported rectangular plates.
References
- Development of analytical and FEM solutions for static and dynamic analysis of smart piezoelectric laminated composite plates on elastic foundation. Journal of Engineering Mathematics (2023).
- Non-linear deflection and stress analysis of laminated composite sandwich plate with elliptical cutout under different transverse loadings in hygro-thermal environment. Curved and Layered Structures (2020).
- Flexure of thick orthotropic plates by exponential shear deformation theory. Latin American Journal of Solids and Structures (2013).
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