Levy-type solution for bending of single-layered graphene sheets in thermal environment using the two-variable plate theory

• Thermomechanical bending response of nanoplates is studied using Levy-type model.
• The nonlocal two-variable plate theory is employed to derive the governing equations.
• The governing differential equations are solved using the state-space concept.
• The present results are very close to those being in the open literature.
• The effects of various parameters on the bending of nanoplates are investigated.

Levy-type solution model is employed to demonstrate the bending response of single-layered graphene sheets subjected to a temperature field as well as external mechanical load. On the basis of Eringen׳s nonlocal elasticity equations incorporated with the two-variable plate theory, the governing differential equations of the thermomechanical response are derived by using the principle of virtual displacement. These equations are converted into a set of first-order linear ordinary differential equations with constant coefficients. The general solution of these equations can be obtained by using the state-space concept. Combinations of simply supported, clamped and free boundary conditions are considered. Comparison of the results with those being in the open literature is made. Numerical results are presented for rectangular sheets with different edge conditions, plate aspect ratios and nonlocal coefficient.