Summary: Structural health monitoring techniques assess structural responses by retrieving total displacement fields encompassing thermal and structural displacement fields. However, techniques to decompose a total displacement field into individual displacement fields – thermal- and structural-load induced fields – have not been explored. To address this research gap, the present work proposes and demonstrates a novel hybrid technique – coupling a low-fidelity FEM and an analytical technique formulated using complex variables. The technique incorporates partial coarse-mesh FEM boundary data with field variables expressions – presented as Laurent series – to compute unknown constants in the series. The technique is illustrated for thermoelastic problems including circular and elliptical rings and a plate with a hole. On the other hand, non-thermoelastic problems of practical utility – a special case of thermoelastic problems – are presented to demonstrate the versatility of the technique. The individual decomposed displacement fields are plotted as contour plots over the domains and are corroborated with high-fidelity FEM. \(L^2\) norms indicate a very good correspondence for thermoelastic problems, indicating the efficacy of the technique. The non-thermoelastic cases show higher deviation but within reasonable limits. Subsequently, the extension of the technique to experiments and evaluation of the stress fields are briefly discussed.