On the role of surface elasticity in nonlinear planar stability of FG porous reinforced nanosize curved beams having different degrees of curvature

The prime target of the present study is to inspect the role of surface elasticity at nanoscale in changing the stability branches as well as lower and upper limit loads of uniformly thermomechanical loaded curved nanobeams having different degrees of curvature. To this end, the classical and surface elastic-based multiple equilibria are predicted for nanosized third-order shear flexible clamped curved beams consisted of through-thickness functionally graded porosity with different graded schemes besides reinforcing by graphene nanofillers. The established nanoscale-dependent nonlinear formulations are then solved numerically with the aid of the isogeometric collocation technique creating a distinct grid of collocation points allocated to the contemplated basis assortments individually via the Greville abscissas. It is deduced that by taking the temperature escalation into account, along with the applied sidewise uniform pressure, the prominence of the surface stress effects on the quantity of upper limit load reduces, while the prominence of them on the quantity of lower limit load enhances. These anticipations become more prominent for a FGP reinforced curved nanobeam possessing less degree of curvature. Accordingly, owning to the small-curved nanobeam, by increasing the amount of temperature escalation from $150°C$ to $300°C$, the prominence of surface stress effects on the upper limit load turns down from $16.90\%$ to $1.51\%$ if $h=15nm$, from $6.76\%$ to $0.38\%$ if $h=30nm$, and from $2.48\%$ to $0.07\%$ if $h=60nm$. While the prominence of surface stress effects on the lower limit load gets higher from $48.69\%$ to $138.25\%$ if $h=15nm$, from $22.70\%$ to $83.95\%$ if $h=30nm$, and from $8.89\%$ to $22.91\%$ if $h=60nm$. Owning to the medium-curved nanobeam, by increasing the amount of temperature rise from $150°C$ to $300°C$, the prominence of surface stress effects on the upper limit load turns down from $14.98\%$ to $12.68\%$ if $h=15nm$, from $7.09\%$ to $6.03\%$ if $h=30nm$, and from $2.84\%$ to $2.41\%$ if $h=60nm$. Alternatively, owning to the large-curved nanobeam, by increasing the amount of temperature escalation from $150°C$ to $300°C$, the prominence of surface stress effects on the upper limit load turns down from $22.30\%$ to $21.15\%$ if $h=15nm$, from $10.38\%$ to $9.82\%$ if $h=30nm$, and from $4.11\%$ to $3.87\%$ if $h=60nm$.