Transverse shear stress relaxed zigzag theory for cylindrical bending of laminated composite and piezoelectric panels

Abstract

• Bending response in elastic laminated panels is greatly improved. • Response in piezolaminated panel with single-material elastic substrate highly improves under electromechanical load. • Response in piezolaminated panel with multi-material elastic substrate improves under electromechanical load. • Improved response is observed in both sinusoidal and uniformly applied loads. • Indicates use of layerwise approximation in transverse displacement instead of global approximation. Cylindrical bending is studied by developing a new zigzag theory which relaxes the zero transverse shear stress condition on the outer surfaces of the panels subjected to transversely applied electromechanical load. The mechanical portion of the transverse displacement approximation in this new shear deformation theory is considered constant as well as non-constant through the development of three models. Unlike the existing zigzag theories which enforce the condition of vanishing transverse shear stresses on outer surfaces of laminates, these new theories relax it. Though the number of primary mechanical variables get increased by four or five or six, the computational cost does not increase appreciably. Approximating the electric potential in each piezoelectric layer as sublayerswise linear, variational principle is applied in deriving equilibrium equations and boundary conditions. Accuracy of the new base model as well as two augmented models is assessed by comparing with elasticity and piezoelasticity solutions. While it is observed that the new base model is highly accurate than the existing zigzag model, the two augmented models do not aid in its further improvement. This is attributed to the fact that layerwise consideration of the transverse displacement, not global consideration, is needed to correctly establish the effect of transverse normal deformation in the laminated composite and smart panel.