Thermal stress around a smooth cavity in a plate subjected to uniform heat flux

TL;DR

This paper presents explicit analytical solutions for thermal stress around a smooth cavity in a plate under uniform heat flux, correcting previous models and analyzing stress concentration effects.

Contribution

It introduces a novel method to explicitly solve the thermoelastic problem for cavities with Laurent polynomial shapes, improving accuracy over prior approaches.

Findings

Explicit solutions match boundary conditions precisely

Identifies and corrects errors in previous literature

Analyzes stress concentration around cavity tips

Abstract

The two-dimensional thermoelastic problem of an adiabatic cavity in an infinite isotropic homogeneous medium subjected to uniform heat flux is studied, where the shape of the cavity is characterized by the Laurent polynomial. By virtue of a novel tactics, the obtained K-M potentials can be explicitly worked out to satisfy the boundary conditions precisely, and the possible translation of the cavity is also available. The new and explicit analytical solutions are compared with the those reported in literature and some serious problems are found and corrected. Finally, some discussions on the thermal stress concentration around the tips of three typical cavities are provided.