Transient analysis of layered beams subjected to steady heat supply and mechanical load

In this study, an analytical model is developed for the analysis of transient temperature, displacements, and stresses in simply supported layered beams. The beam is suddenly heated from the top and bottom surfaces by external steady heat sources and is subjected to a mechanical load. The temperature in each layer is variable along the thickness and follows the one-dimensional (1-D) transient heat transfer equation. The Laplace transform approach is used to obtain the transient temperature field in the beam. The thermoelastic constants of the beam are temperature-dependent. Dividing every layer into a series of thin slices, the temperature and the thermoelastic constants for each slice can be considered uniform. The two-dimensional (2-D) thermoelasticity theory is adopted to derive the governing equations of displacements and stresses in each slice. The transfer matrix method is applied to obtain the displacement and stress solutions for the beam. As an example, the distributions of transient temperature, displacements, and stresses in a three-layer beam are studied. The effects of the temperature dependent thermoelastic constants on the mechanical behavior of the beam are discussed in detail.