Thermal and thermo-mechanical solution of laminated composite beam based on a variables separation for arbitrary volume heat source locations

In this work, a method to compute explicit thermal solutions for laminated and sandwich beams with arbitrary heat source location is developed. The temperature is written as a sum of separated functions of the axial coordinate x, the transverse coordinate z and the volumetric heat source location x₀. The derived non-linear problem implies an iterative process in which three 1D problems are solved successively at each iteration. In the thickness direction, a fourth-order expansion in each layer is considered. For the axial description, classical Finite Element method is used. The presented approach is assessed on various laminated and sandwich beams and comparisons with reference solutions with a fixed heat source location are proposed. Based on the accurate results of the thermal analysis, thermo-mechanical response is also addressed using also a separated representation.