Nonlinear deformation of rotating functionally graded trapezoidal microplates in thermal environment

Abstract

A comprehensive study of the size-dependent nonlinear thermal deformations of rotating trapezoidal functionally graded (FG) microplates is presented herein. To incorporate the size effects and transverse shear deformations, the modified strain gradient theory (MSGT) in conjunction with a four-variable refined plate theory is employed. The mathematical model is developed under the von Kármán geometric nonlinearity assumptions. It is assumed that the properties of the constituent materials are temperature-dependent and their composition changes gradually in the thickness direction. By employing the Chebyshev-Ritz method, the system of nonlinear equations governing the nonlinear deformation of rotating trapezoidal FG microplates is derived. The thermal loadings are induced by steady-state non-uniform temperature rise across the microplates thickness. The obtained nonlinear equations are solved numerically using Broyden’s method. After validating the approach, the influences of angular velocity, length scale parameter, material gradient index, and thickness-to-length ratio on the temperature rise-deflection paths of the rotating trapezoidal FG microplates are investigated. Findings show that the temperature dependence of material properties has significant on the results and should be considered to achieve accurate results.