Three-dimensional thermal and stress distribution in isotropic plates with sharply radiused V-notches

This work presents a comprehensive analytical study of thermal stress fields in three-dimensional bodies containing sharp and sharply radiused V-notches. For the first time, an exact solution is derived for the stationary temperature distribution and associated thermal fluxes in V-shaped notches with a finite root radius, using a conformal mapping and dedicated curvilinear coordinates. Building upon this thermal field, the three-dimensional stress distribution is obtained by decoupling in-plane and out-of-plane components, revealing their coupling under thermal loadings. This demonstrates that the framework and equations previously derived for purely mechanical problems can also be applied to thermally induced stresses. All analytical results are validated against high-fidelity finite element simulations, confirming their accuracy and practical relevance. The influence of key geometric parameters, such as plate thickness, notch opening angle, and root radius, is then systematically examined. The work provides new insights into the three-dimensional behavior of stresses near rounded notches and offers practical tools for assessing structural integrity under thermal gradients.