Morphology-Embedded Synergistic Optimization of Thermal and Mechanical Performance in Free-Form Single-Layer Grid Structures

Free-form grid structures offer both aesthetic appeal and structural efficiency in long-span roof design and application, yet the potential of morphological design to optimize thermal performance has been long overlooked. This study proposes a multi-objective synergistic optimization framework which can improve the thermal environment and mechanical performance simultaneously for the roof. Focusing on public buildings in hot–humid climates, the research investigates the impact of roof geometry on indoor temperature under extreme thermal loading conditions and long-term thermal loading conditions. Furthermore, the evolution of thermal performance during mechanical performance-driven surface optimization is systematically analyzed. Subsequently, a dynamic proportional adjustment factor is introduced to explore the performance of the optimized results under different performance weights, with thermal and mechanical performance serving as the optimization objectives. Results demonstrate that thermal performance-driven optimization generates saddle-shaped free-form surfaces with alternating peak–valley configurations to achieve self-shadowing effects, reducing indoor temperature by approximately 2 °C but significantly compromising structural stiffness. Conversely, strain energy minimization yields moderate indoor temperature reductions, revealing a positive correlation between strain energy decrease and thermal performance improvement. In the multi-objective optimization considering thermal and mechanical properties, when the strain energy ratio is 0.5–0.7 (optimization balance zone), the indoor temperature decreases, while the structural stiffness and stability bearing capacity increase. This study provides a morphological–structural–environmental synergistic design reference for low-carbon long-span building roofs.