On the accuracy of recent global–local theories for bending and vibration of laminated plates

The 11-variable global–local theory (GLT) was proposed in 1997 with the purpose of accurately predicting transverse stresses in laminated structures directly from the constitutive equations. However, the theory has so far been tested only for composite laminates made of a single material. This study critically examines the accuracy of the GLT for static and dynamic response of plates for a variety of laminate configurations. The recently developed zigzag-local theory (ZLT), with nine primary variables, which also has the capability to calculate transverse shear stresses from constitutive equations, is extended for dynamic analysis and assessed. The comparison with the exact 3D elasticity solutions reveals that the GLT is good only for laminates with upto three layers. For multi-material composite laminates and sandwich laminates with more than three layers, its prediction is poor and even worse than the existing five-variable zigzag theory (ZIGT), not only for transverse shear stresses, but also for displacements and natural frequencies. The ZIGT, on the other hand, yields very accurate results for displacements, inplane stresses and natural frequencies for all laminate configurations. The ZLT is even better with the ability of predicting transverse shear stresses directly from the constitutive equations with good accuracy for any laminate lay-up.