Spline Continuity and THB-Spline Local Refinement in Thermomechanical Analysis with Localized Heat Sources

Thermomechanical simulations with localized heat sources are affected by the approximation spaces used for temperature and displacement. This paper examines spline continuity and truncated hierarchical B-spline (THB-spline) local refinement on a shared physical mesh. Degree-p displacement is combined with degree-p or degree-(p−1) temperature, and temperatures are evaluated at common Gauss points to compute thermal strains. The interpretation distinguishes directional polynomial degrees on parametric elements from interelement continuity and geometry-mapping effects. A linear thermoelastic benchmark with a body source constructed from a Mokrov-type target temperature profile compares B-splines and Bézier elements, together with ring and central THB-spline refinement. A constant-property, plane-strain plate benchmark with a moving heat source extends the comparisons to thermoelastoplastic response, including thermal histories and path-based THB refinement. Reduced-order temperature generally decreases visible stress oscillations and lowers the relative sampled-line stress error in 18 of 24 matched Mokrov-benchmark comparisons; six comparisons have larger errors. In the moving-heat-source thermoelastoplastic benchmark, path-based THB refinement concentrates resolution near the source trajectory using approximately 45% of the field unknowns of uniform B-splines, while reduced-order temperature produces smoother stress profiles on the same hierarchical mesh.