Thermal buckling analysis of nano composite laminated and sandwich beams based on a refined nonlocal zigzag model

Abstract

A refined nonlocal zigzag model for thermal buckling analysis of nano composite laminated and sandwich beams is proposed in this study based on a refined zigzag theory and Eringen’s nonlocal theory. Firstly, present model satisfies the stress-free and continuity conditions a priori by introducing the piecewise-linear zigzag functions and a preprocessing, such that the transverse shear correction factors are not needed. In the preprocessing, accurate and continuous transverse shear stresses are obtained with the aid of the general mixed variational principle, which can be solved simultaneously with other stresses in the governing equations. This is quite different from the previous post-processing. Subsequently, thermal buckling problems of nano composite laminated and sandwich beams are analytically solved in simply supported boundary conditions. The degenerated results without small effect indicate that the non-dimensional critical loads and critical temperatures have a good agreement with the 3D elasticity solutions and previous results, which demonstrate the accuracy and reliability of present model. Moreover, it is observed that the small effect of the critical temperatures can be effectively captured by Eringen's differential constitutive law (EDCL), which shows the small effect decreases the critical temperature by weakening the stiffness of the beam. Finally, the effects of different thermal expansion coefficients, laminations, geometric sizes and beam theories are discussed. The results show that present model is robust in the arbitrary layouts for both of composite and sandwich structures, which may have some referential significance to Micro-Electro-Mechanical Systems (MEMS) sensors and actuators.