On the mechanical behavior of a functionally graded micro-beam subjected to a thermal moment and nonlinear electrostatic pressure

In the present work, mechanical behavior of a functionally graded cantilever micro-beam subjected to a nonlinear electrostatic pressure and temperature changes has been studied. It has been assumed that the top surface is made of pure metal and the bottom surface from a metal–ceramic mixture. The ceramic constituent percent of the bottom surface varies from 0% to 100%. In addition to the Volume Fractional Rule of material, exponential function has been used for representation of continuous gradation of the material properties through micro-beam thickness. Attention being paid to the ceramic constituent percent of the bottom surface, five different types of FGM micro-beams have been investigated. Nonlinear integro-differential thermo-electro mechanical equation based on Euler–Bernoulli beam theory has been derived and solved using Step-by-Step Linearization Method and Finite Difference Method. The effects of temperature changes and the electrostatic pressure on the deflection and stability of FGM micro-beams having various amounts of the ceramic constituent have been studied and normal stress distributions in the cross section along the beam thickness have been given and compared with a classic metal beam.