Large thermal deflections of Timoshenko beams under transversely non-uniform temperature rise

Geometrically non-linear deformation of axially extensional Timoshenko beams subjected mechanical as well thermal loadings were characterized by a system of 7 coupled and highly non-linear ordinary differential equations, which results in a complicated two-point boundary-value problem. By using shooting method this kind of problem can be numerically solved efficiently. Based on the above-mentioned mathematical formulation and numerical procedure, analysis of large thermal deflections for Timoshenko beams, subjected transversely non-uniform temperature rise and with immovably pinned–pinned as well as fixed–fixed ends, is presented. Characteristic curves showing the relationships between the beam deformation and temperature rise are illustrated. Especially, the effects of shear deformation on the bending and buckling response are quantitatively investigated. The numerical results show, as we know, that shear deformation effects become significant with the decrease of the slenderness and with the increase of the shear flexibility.