热结构瞬态响应的耦合灵敏度分析方法与优化设计

研究结构瞬态热变形和热应力的灵敏度分析方法及其优化设计,灵敏度计算给出了直接法和伴随法两种算法.考虑了温度场的耦合作用,在直接法中需要计算温度场对设计变量的导数,在伴随法中需要计算热载荷对温度场的导数.数值算例验证了该方法的精度.伴随法在应用程序中的实现,为大型结构优化提供了高效率的灵敏度计算方法.

COUPLING SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION OF THERMO-STRUCTURAL TRANSIENT RESPONSES

The numerical methods of sensitivity analysis and design optimization for structures with transient thermal deformation and thermal stresses as design criterions are studied in this paper. In the sensitivity analysis of thermal stress and deformation, two kinds of algorithms of the direct method and the adjoint method have been proposed and the coupling effect of temperature field is considered. To deal with the coupling effect of temperature field, the derivatives of temperature field with respect to variables are required in sensitivity calculation for thermal loads and thermal stresses in the direct method, while the derivatives of thermal load with respect to the temperature field are required in the adjoint method. A numerical example is given to demonstrate the effectiveness of shape design optimization reducing the thermal stress, evaluate the accuracy of sensitivity analysis methods, and show the effect of temperature field derivatives in the coupling sensitivity analysis. The implementation of the adjoint method in application software provides efficient sensitivity analysis for large-scale problems of structural design optimization.