Effects of Casimir Force and Thermal Stresses on the Buckling of Electrostatic Nanobridges Based on Couple Stress Theory

In this paper, the thermal and size effects on the buckling behavior of a nanobeam symmetrically located between two electrodes, subjected to the influence of the nonlinear external forces including electrostatic and Casimir attractions, have been investigated. Based on the modified couple stress theory and by using Hamilton's principle, the governing equation is derived from Euler-Bernoulli beam model and the non-dimensional critical buckling load is presented. In order to achieve linearization the equations, instead of nonlinear forces, their corresponding Maclaurin series expansions are used. Also, the differential quadrature method is utilized to solve the buckling equations numerically. Finally, the material length scale parameters (the size effects), the electrostatic and Casimir nonlinear forces, the temperature change, as well as the effect of the initial gap between beam and fixed electrodes on the buckling load are studied. The results indicated that by increasing the forces dependent on the displacement such as Casimir and electrostatic, the buckling load decreases. However, increasing the material length scale parameters leads to an increase in the buckling load value. Meanwhile, the initial gap does not significantly affect the buckling load. Furthermore, the non-dimensional critical buckling load becomes higher with the temperature change increasing.