热-应力耦合结构灵敏度分析方法  

SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION OF THERMAL-STRESS COUPLED STRUCTURES

作　　者：顾元宪[1] 赵红兵[1] 陈飚松[1] 亢战[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,大连116024

出　　处：《力学学报》2001年第5期685-691,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(19872017;59895410);国家重点基础研究专项经费(G1999032805)资助项目

摘　　要：研究稳态／瞬态热传导灵敏度分析、以及热与机械荷载同时作用的热结构应力灵敏度分析问题．考虑了温度场随设计变量的变化及其对热应力的影响，提出温度场与结构热应力耦合问题的灵敏度计算方法．特别指出了热－应力耦合灵敏度分析中温度场导数的影响；说明了在热－应力耦合结构灵敏度分析中必须考虑耦合灵敏度．在应用软件系统ＪＩＦＥＸ中实现了所提出的方法，数值算例验证了灵敏度算法的精度．Design sensitivity analysis concerns the relationship between the design variables and structural response and state variables. Sensitivity information is very import for design opti- mization, inverse problem, stochastic analysis and probability analysis of engineering structures. This paper addresses the research on the sensitivity analysis of thermal structures subjected to the steady/transient heat conduction and mechanical load. The formulas of sensitivity analysis for steady/transiellt heat conduction are presented in conjunction with semi-analytical method. The conventional time difference method, θ-time difference scheme, is employed to solve the sen- sitivity equations of transient heat conduction. It is pointed out that the method of sensitivity analysis for heat conduction has good numerical accuracy and computational efficiency. The vari- ation of temperature field and its influence on the thermal stresses are considered. The thermal deformation is Viewed as a steady or quasi-static process. The method of sensitivity analysis for coupled thermal stresses has been proposed. The coupling effect of the temperature derivatives with respect to design variable on the thermal stress sensitivity is particularly presented. Detailed analysis shows that the coupling factor makes a great effect on the sensitivities of thermal stresses. The methods presented in the paper can be applicable for shape and size design variables. Two numerical examples are given to demonstrate the correctness of the methods. One is the shape sensitivity analysis of a plate subjected to different ratio of thermal load and mechanical load. The other is the sensitivity analysis of sectional shape optimization of train wheel. Numerical results validate the methods and show that for design optimization of thermal-stress coupling structures, the coupling sensitivity should not be neglected.

关 键 词：灵敏度 热传导 热应力 热结构 耦合系统 

分 类 号：O342[理学—固体力学] O551.3[理学—力学]