Transient Thermoelastic Analysis of a Multi-layered Oblate Spheroidal Shell with Internal Heat Generation

Abstract

The principal aim of this paper is to investigate the thermoelastic responses in a generalised oblate spheroid subjected time-independent volumetric heat sources in each layer and sectional heat supply on the inner and outer curved surfaces. The closed-form solution is obtained for transient temperature distributions by establishing Sturm-Liouville integral transform considering series expansion function in terms of an eigenfunction of Sturm-Liouville boundary value problem for the composite region consisting of multilayered composites in an oblate spheroidal coordinate system. The relations obtained in this paper can be applied to any arbitrary boundary and initial conditions to avoid structural failure due to thermal stress response. Some results which are derived using computational tools are accurate enough for the practical purpose were depicted graphically. The three-layer elliptic region has been computed numerically and exhibited in a graphical form, by using dimensionless values and therefore discussed.