  This paper developes a theoretical model directed towards investigation of
the static pull-in instability of functionally graded (FG) electrostatic
nano-bridge under the influence of electrostatic and van der Waals (vdW) forces
in thermal environment via nonlocal strain gradient theory (NLSGT) of
elasticity and Euler-Bernoulli beam theory in conjunction with the nonlinear
geometric effect resulting from mid-plane stretching. The material properties
of FG nano-beam are assumed to vary gradually along the thickness direction
according to simple power-law form. With the purpose of eliminating the
coupling between the stretching and bending due to the asymmetrical material
variation along with the thickness, a new surface reference is introduced. The
nonlinear integro-differential governing equation is derived utilizing minimum
total potential energy principle, linearized by means of the step-by-step
linearization method (SSLM) and solved by Galerkin based weighted residual
method. The numerical investigations are performed while the emphasis is placed
on studying the effect of various parameters including nonlocal parameter,
material characteristic length scale, material gradient index, the thermal
effect and intermolecular force on the static pull-in instability of FG
nano-beam. To establish the validity of the present formulation, a comparison
is conducted with experimental and numerical results reported in previous
studies.
