Surface stress size dependency in nonlinear thermomechanical in-plane stability characteristics of FG laminated curved nanobeams

Abstract

In the present exploration, the effect of surface stress type of size dependency on the nonlinear in-plane stability characteristics of functionally graded (FG) laminated composite curved nanobeams subjected to uniform radial pressure together with a temperature rise is examined. To accomplish this motivation, the Gurtin-Murdoch continuum elasticity is applied within a higher-order shear flexible curved beam theory in the presence of geometric type of nonlinearity. The effective properties of the employed nanocomposites are approximated via the Halpin-Tsai homogenization scheme corresponding to different lamination patterns and are considered in the principle of virtual work to establish the surface elastic-based nonlinear differential equations of the stability problem. It is found that by taking the surface stress effect into account, the values of the radial load related to the first and second bifurcation points get larger. Also, it causes to increase the curved beam deflection associated with the first bifurcation point, while it leads to decrease the radial deflection at the second bifurcation point. Accordingly, the effect of surface stress type of size dependency resulted in a reduction in the slope of bifurcation path related to the nonlinear radial load–deflection equilibrium curve of a curved nanobeam. It can be also observed that the temperature rise causes to increase the radial loads associated with the upper limit and the first bifurcation points, while it leads to reduce the values of radial load related to the lower limit and the second bifurcation points. In this regard, there is a unique intersection point as all equilibrium curves traced for different temperature rises pass through that.