Static analysis of highly anisotropic laminated beam using unified zig-zag theory subjected to mechanical and thermal loading

Abstract

In the present study, static behavior of short hybrid laminate beams was investigated using a unified zig-zag theory (ZZT) containing various beam theories as special cases. This theory satisfies transverse shear stresses continuity in the interface of layers via piece-wise continuous arbitrary shape functions. The principle of virtual work was employed to derive unified equilibrium equations and suitable boundary conditions. The present theory obviates the need for stress recovery for continuous transverse stresses. A general solution was presented to analyse high transversely anisotropic laminates under several kinds of transverse loads (general lateral, sinusoidal and point load) and non-linear thermal loads. The validity of this model is demonstrated by comparison of its predictions and good agreement with published results in literature. Numerical examples were given to investigate the impact of the transverse anisotropy on displacement, strain and stress fields through the thickness. The results show that the piece-wise continuous exponential and sinusoidal shape functions provide more accurate transverse stress distribution in comparison with other shape functions. In addition, the results show that the continuity of transverse shear stress through the thickness plays an important role in analysing transversely anisotropic laminated beams. A comparison of present ZZT and existing exact elasticity solutions shows that the current theory is simple and efficient.