Thermal Stresses in Multilayer Spherical Vessels due to Transient Temperature

Abstract

This paper presents an analytical study of a transient, spherically symmetric thermoelastic response of a multilayer spherical vessel subjected to combined thermal and mechanical loading. The vessel consists of a load-bearing core, an intermediate composite layer, and an external thermal insulation coating. Within the quasi-static approximation, the temperature field is obtained independently by solving the transient heat conduction problem governed by Fourier’s law and is subsequently introduced into the mechanical formulation as a prescribed thermal load. The mechanical problem accounts for internal pressure and thermally induced strains, while the intermediate layer is modeled using a homogenization approach that captures its effective macroscopic properties without explicit representation of the underlying microstructure. An efficient direct integration method is employed to derive closed-form expressions for the stresses and the radial displacement in each layer, allowing for a consistent treatment of material inhomogeneity and multilayer interfaces. The proposed formulation enables a systematic investigation of the effects of the intermediate layer characteristics and the thermal insulation coating parameters on the transient stress–strain state of the vessel. The results demonstrate that appropriate selection of the intermediate layer properties can significantly reduce peak thermal stresses and alter their temporal evolution, while the insulation coating primarily influences the magnitude and location of maximum stresses by modifying the temperature gradients. The developed analytical framework provides a practical tool for designing and optimizing multilayer spherical pressure vessels that operate under transient thermal conditions.