Thermal Stability Analysis of Nonlocal Temperature-Dependent Functionally Graded Tapered Timoshenko Nanobeam

Abstract

Analysis on buckling behavior of functionally graded (FG) Timoshenko nanobeam with cross-sectional variation induced by nonlinear temperature (NLT) field has been presented on the basis of first-order shear deformation theory in conjunction with Eringen's nonlocal elasticity theory. The cross-sectional nonuniformity of the beam is assumed to arise due to linear variation in thickness along the length. The material composition of the beam varies in thickness direction according to a power-law function and depends upon temperature. For the first time in case of nanobeam, the dependency of temperature has been incorporated in the analysis by using an iterative procedure for computing the material properties at current temperature instead of ambient temperature which gives a more accurate approximation for the temperature-dependent material properties. The governing equations of buckling for such a beam model have been developed using minimum energy principle and solved numerically using generalized differential quadrature method (GDQM) for three different edge conditions. A significant contribution of nonuniformity in the cross section on thermal buckling behavior of Timoshenko nanobeam has been noticed.