• • The optimized SiO2/ZrO2 aerogel (θ = 40°, x = 1.3 mm) achieves an ultra-low thermal conductivity of 30.2 mW·m−1·K−1, enabling superior insulation for high-temperature applications.
• • The arctangent-topological design (αn = 26.6°, n = 2) increases compressive strength by 114% to 341.7 kPa (at 24.6% fracture strain) while maintaining a low thermal conductivity of 33.9 mW·m−1·K−1, addressing the brittleness of inorganic aerogels.
• • The aerogels withstand temperatures above 1000 °C, as demonstrated in flame nozzle tests, confirming their suitability for extreme thermal environments such as engine combustion chambers.
• • Finite element simulations (COMSOL) validate the experimental thermal and mechanical performance, providing a predictive tool for optimizing aerogel architectures.
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