A high-order theory of a thermoelastic beams and its application to the MEMS/NEMS analysis and simulations

Abstract

A high-order theory for beams based on expansion of the two-dimensional (2-D) equations of thermoelasticity and heat conductivity into Legendre polynomials series has been developed. The 2-D equations of thermoelasticity and heat conductivity have been expanded into Legendre polynomials series in terms of a thickness coordinate. Therefore, all equations of thermoelasticity and heat conductivity including Hooke’s and Fourier’s laws have been transformed into corresponding equations for coefficients of Legendre polynomials expansion. Then, the system of differential equations in terms of displacements and temperature and boundary conditions for the coefficients of Legendre polynomials expansion has been obtained. Cases of the first and second approximations have been considered in detail. For obtained boundary-value problems, a finite element method has been used and numerical calculations have been done with COMSOL Multiphysics and MATLAB. Developed theory has been applied for study stress–strain state and temperature distribution in the microelectromechanical and nanoelectromechanical systems and structures.