A Boundary Element Formulation for Thermomechanical Contact Problems with Internal Linear Heat Sources Applied to Layered Floor Systems

A three-dimensional steady-state thermomechanical contact formulation based on the Boundary Element Method is presented for the analysis of systems involving internal linear heat sources. The formulation consistently couples thermal conduction and thermoelastic contact effects within a boundary integral framework and is suitable for layered configurations governed by interface interactions. The approach is first validated through benchmark problems and subsequently applied to the analysis of a radiant floor system composed of a self-levelling compound and a surface floor covering supported by an elastic foundation. Linear heat sources representative of heating pipes are embedded within the compound layer, and the influence of their vertical position on the thermal and mechanical response of the system is investigated. The results show that the mean surface temperature exhibits an approximately linear dependence on the depth of the heat sources, indicating a high sensitivity of the thermal response to installation parameters. An extended scenario accounting for constrained displacements at the upper edge is also analysed in order to represent more realistic boundary conditions. Under these conditions, partial interface separation induced by thermal expansion leads to a reduction in the heat transferred towards the surface and to lower surface temperature levels. The proposed formulation provides a physically consistent and efficient framework for the analysis of thermomechanical contact problems with localized heat sources, offering an alternative tool for the investigation of layered floor systems and related engineering applications.