Bistability of functionally graded carbon nanotube-reinforced composite plates

Abstract

In this thesis, we introduce single-walled carbon nanotubes (SWCNTs) as the reinforcement and discuss the thermally-induced bistable behavior of the carbon nanotube-reinforced composite (CNTRC) plates. The volume fraction of the SWCNTs is relatively low and functionally graded (FG) along thickness direction by following an exponential function. The bistable behavior of the plate is caused by the residual stresses in the plate after cooled from elevated curing temperature to room temperature. In this thesis, an analytical model developed by Dano and Hyer is used for the approximations of the mid-plane strains and the deflection of the plate. After that, we introduce Rayleigh-Ritz model for minimizing the total potential energy and obtain bistable states of the plates. Based on Hyer’s model, we also develop an extended model which uses high-order approximation functions for the mid-plane strains and the deflection to verify the accuracy of the Hyer’s model. The objectives of the thesis are to develop MATLAB programs which can be used for solving similar problems and to find out the relations between the occurrence of the bistability and the initial temperature, the dimension of the plate and the exponent in the expression of the FG distribution for SWCNTs. Moreover, this thesis is also aimed to verify that the Hyer’s model is feasible for dealing with the bistability of CNTRC plate by conducting a comparison between Hyer’s model and the extended model. Two kinds of CNTRC plates – the FG [0/90] CNTRC plate and the FG composite plate with rotating SWCNTs are discussed in this thesis. The results show that higher initial temperature, larger width-to-thickness ratio of the plate and larger value of the exponent are beneficial for the occurrence of the bistable behavior of the CNTRC plate with relatively low proportion of SWCNTs. Besides, the Hyer’s model is precise enough for predicting the bistable behavior of the CNTRC plate, which is proved by the comparison with the extended model.