摘要
航天是一个融合了各领域技术的高精尖科技工程，空间结构设计是航天器稳定和可靠工作的基础，能够保证航天器在恶劣的空间环境中工作。其中比较突出的问题是如何量化热辐射对结构振动产生的影响，故分析结构在温度场和结构位移场等多场环境下动力响应具有重要工程意义。本文以航天器中常用的平板结构作为研究对象，考虑其在太阳光辐射作用下产生热应力导致热变形，而结构变形使得接收到的太阳光热流变为交变热流，进一步影响结构的热变形，将这种热和结构之间的相互作用视为热-结构耦合。因此在考虑结构部分物理参数为随机场的情况下，有必要对空间中的平板结构热-结构耦合的动力响应展开研究，具体工作如下：
（1）查阅国内外大量文献发现，在空间结构受到“阴影-光照”的突然变化后，会发生热致振动产生热-结构耦合现象，且结构物理参数的随机性会极大影响其动力响应。同时，对本文中要用到的相关理论，如，随机场、热力学、结构动力学以及等几何分析方法等开展了研究。
（2）使用Mindlin平板理论，建立空间结构在热-结构耦合下的有限元模型，其过程为：①将平板结构进行有限元网格划分，并施加力学控制方程和边界条件获得动力学微分方程；②将结构的有限元网格扩充为热传导有限元网格,并构建其热传导微分方程；③在时域内分别用间差分法和Newmark-β法对热传导和结构动力学微分方程进行展开，然后对温度场和结构位移响应交替迭代计算，获得每一时刻的温度响应和位移响应。通过算例分析表明：当空间中平板结构突然经历“阴影-光照”的转化过程后，会诱发结构振动，随后振幅逐渐减小，振动趋于平缓，最后变成稳定的振动。之后，考虑结构的弹性模量和质量密度为随机场变量，将其用Karhunen-Loeve法进行展开，构建随机热-结构耦合有限元模型，通过算例抽样计算并分析每一个随机场参数对结构动力响应特征值的影响。
（3）以平板结构的非均匀有理B样条几何模型为基础，使用等几何分析方法推导得到热传导微分方程以及动力学微分方程，实现使用CAD模型直接进行CAE分析的过程，进一步对模型进行细化，并构建材料的弹性模量和质量密度是随机场的热-结构耦合随机等几何分析模型。首先，使用数值的方法对微分方程进行展开计算得温度场、位移场；然后，将等几何分析的结果与有限元结果进行对比分析，表明了所建模型的准确性；最后，对不同随机场参数进行抽样统计分析，获得不同随机场参数对结构动力响应的影响程度，结果表明弹性模量随机场的标准差影响最大。
关 键 词：热-结构耦合， 有限单元法， 随机场， K-L展开， 等几何分析
ABSTRACT
Astronautical industry is a high-precision science and technology engineering that integrates technologies in various fields, and space structure design is the fundation of the stable and reliable operation of spacecraft, which ensuring that it is capable of working in harsh space environments. One of the more prominent problems is how to quantify the influence of thermal radiation on structural vibration, it is of great engineering significance to analyze the dynamic response of the structure in a multi-field environment such as temperature field and structural displacement field. In this paper, the commonly used plate structure in spacecraft is taken as the research object, and thermal stress is generated and thermal deformation is accordingly induced by considering the action of solar radiation. The deformation makes the received solar heat flow into alternating heat flow, which further affects the thermal deformation of the structure, and the interaction between heat and structure is considered as the thermal-structure coupling. And the interaction between the above heat and structure is named as thermal-structure coupling. Therefore, it is necessary to study the influence of the random field parameters in space on dynamic response under thermal-structure coupling with random fields’ physical parameters of the plate structure considered. The specific work is as follows:
(1) Consulting a large number of domestic and foreign documents, it is found that thermal-structure coupling is produced by the thermally induced vibration, and the dynamic response is affectd by the randomness of structure's physical parameters when the spatial structure experiences a sudden change of "shadow-light". At the same time, the relevant theories used in this work are studied, such as random field, thermodynamics, structural dynamics as well as isogeometric analysis methods.
(2) The finite element model of a space structure under thermal-structure coupling is established by using the Mindlin plate theory, and the process is as follows: ①Mesh the plate structure by finite element method, and apply mechanical control equations and boundary conditions to obtain dynamic differential equations; ②Extend the finite element grid to finite element mesh of heat conduction and construct its heat conduction differential equations; ③In the time domain, expand the differential equations of heat conduction and structural dynamics by applying the difference method and the Newmark-β method respectively, and then calculte the temperature field and structural displacement response in an interative manner to obtain the temperature response and displacement response at each moment. The numerical example shows that the plate structure in the space, after a sudden "shadow-light" transformation process, could induce structural vibration, and subsquently its amplitude gradually decreases with a gentle vibration, which leading to a stable vibration. After that, the elastic modulus and mass density of the structure are considered as random field variables and expanded by the Karhunen-Loeve method, which is used to construct the finite element model under random thermal-structure coupling.
(3) Based on the NURBS (Non-Uniform Rational B-Spline) spline geometric model of the plate structure, the IGA (Isogeometric Analysis) method is used to derive the heat conduction differential equation and dynamic differential equation to realize the process of directly performing CAE analysis using the CAD model. Furthermore, the elastic modulus and mass density of the material are regarded as random fields, and then the isogeometric analysis model under thermal-structure coupling is constructed by refining the NURBS spline geometric model. Firstly, numerical methods are used for expanding the differential equation to calculate the temperature field and displacement field; Then, the results of IGA are compared with that of finite element analysis, which indicate the accuracy of the built model; Finally, different random field parameters are performed with sampling statisticcal analysis to obtain the degree of influence of different random field parameters on the dynamic response of the structure. The results show that the mean square error of the elastic modulus random field holds the greatest influence.
Keywords: thermal-structure coupling, finite element method, random fields, K-L expansion, isogeometric analysis
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