Parametric Optimization of Thermoelastic Energy Harvesting Systems under Low-Grade Thermal Cycling

This study presents a physics-based parametric optimization framework for thermoelastic energy harvesting from cyclic temperature variations using a cylindrical AISI 4340 steel rod. The model couples thermoelastic force and displacement, Euler buckling and yielding constraints, lumped-capacitance heat transfer, and mass-power multi-objective optimization. The feasible design space was evaluated as a function of rod diameter, length, temperature change, and load-transfer parameter. The results show that Euler buckling governs the practically relevant portion of the design space at moderate temperature changes, whereas yielding becomes increasingly restrictive at higher thermal loads. The Pareto-optimal solutions exhibit a clear mass-power scaling law, with the analytical prediction Pavg ∝ m2/3 closely reproduced by the numerical fit (n = 0.66717, R² = 0.999999). Under the baseline condition λ = 0.50, the maximum-power design produces approximately 0.16624 W, while a distance-to-ideal criterion identifies a substantially lighter compromise design with m = 223.0 kg and Pavg = 0.09231 W. Refined optimization gives λopt = 0.473 and Pmax = 0.170454 W, indicating a power penalty of only 2.47% when the simpler λ = 0.50 condition is used. Grid-refinement tests show changes below 0.006% in maximum power and below 0.5% in the compromise-design mass between the 250 × 250 and 500 × 500 grids. The results establish compact scaling and optimization rules for balancing structural stability, thermal response, mass, and average mechanical power in thermoelastic energy-harvesting elements.

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