New symplectic analytic solutions for buckling of CNT reinforced composite rectangular plates

This paper presents new analytic solutions for buckling of non-Le ' vy-type carbon nanotube (CNT) reinforced composite rectangular plates, including cantilever, free, and clamped ones. The buckling problems of such types of plates cannot be handled by some conventional analytic methods through expressing mechanical quantities in pre-defined solution forms, which, however, is excluded by the present analytic symplectic superposition method. The present method not only provides a more rigorous solution procedure but also enables more types of plates to be analytically solved. The governing partial differential equation is first expressed in the Hamiltonian system-based symplectic space, and then the variable separation as well as the symplectic eigen expansion are utilized to analytically solve two elementary buckling problems. By a skillful superposition of the elementary solutions, the eventual buckling solutions are obtained. Comprehensive buckling load/mode results are tabulated as new benchmarks. With the new analytic solutions, the parametric studies on CNT distributions, CNT volume fractions, aspect ratios, and boundary conditions are conducted to reveal the effects on the plate buckling performance.

Automated summary

This paper presents a new analytic symplectic superposition method for solving the buckling problems of non-Levy-type CNT-reinforced composite rectangular plates. By expressing the governing equation in the Hamiltonian system-based symplectic space and utilizing variable separation and symplectic eigen expansion, the paper obtains two elementary buckling solutions and then combines them to obtain the final buckling solutions. The new analytic solutions are used to conduct parametric studies on CNT distributions, CNT volume fractions, aspect ratios, and boundary conditions to reveal their effects on the plate buckling performance.