Thermo-mechanical analysis of carbon nanotube based functionally graded Timoshenko beam

This analytical work deals with prediction of the stresses developed in a Functionally Graded Timoshenko Beam that has been reinforced with Carbon Nanotubes (CNTs), which is subjected to thermal and mechanical loads. High temperatures have been applied to the upper and lower surfaces of the beam with a certain temperature difference between the two layers for the formation of a temperature gradient. The physical properties of the constituent elements of the beam material vary with temperature and further a variation in temperature leads to development of stresses in a beam. The constituent materials are alumina as the ceramic material, as well as the matrix material, of the functionally graded beam and single walled CNTs as the reinforcement material. Further the physical properties of the beam would vary along the thickness direction according to the volume fraction of the constituents of the beam. In this analysis the volumetric fraction varies according to power law. Temperature-dependent and temperature-independent material properties were obtained layer wise by dividing the entire thickness of the beam into ten layers. Thermal stresses were obtained using temperature-dependent and temperature-independent material properties for each layer for different slenderness ratios and compared