Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation

The objective of the present paper is to investigate the bending, buckling and vibration behaviors of carbon nanotube-reinforced composite (CNTRC) beams. The beams resting on the Pasternak elastic foundation, including a shear layer and Winkler spring, are considered. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are estimated by using the rule of mixture. Various shear deformation theories are employed to deal with the problems. The mathematical models provided in this paper are numerically validated by comparison with some available results. New results of bending, buckling and vibration analyses of CNTRC beams based on several higher-order shear deformation theories are presented and discussed in details. Several aspects of beam types, spring constant factors, carbon nanotube volume fraction, etc., are taken into investigation.