Nonlinear Thermal Stability of Rotating Pre-twisted Temperature-Dependent FG Microblades

Abstract

The main objective of this study is to investigate the post-buckling thermal load–deflection path of rotating pre-twisted microblades/beams made of temperature-dependent functionally graded materials (FGMs) via nonlinear non-classical first-order shear deformation theory (FSDT). To this end, modified strain gradient theory (MSGT) as well as the von Karman geometric nonlinearity is used to develop the size-dependent nonlinear beam theory. Thermal loading is exerted by providing nonlinear (non-uniform) temperature rise across the microbeam thickness at steady-state condition. By using the principle of virtual work and Ritz method, the discretized form of nonlinear equations governing the post-buckling behavior of rotating pre-twisted functionally graded (FG) microbeams is achieved. To solve the obtained nonlinear equations numerically, Broyden’s method is employed. The effects of twist angle along the beam axis, angular velocity, index of the material gradient, length-scale parameter and thickness-to-length ratio on the post-buckling path of FG microbeams are carefully investigated. Findings show that making a correct assumption about the temperature dependence of material is an important factor to increase accuracy of results.