基于界面元法及虚拟激励法的随机热传导分析

The uncertain factors in engineering result in the randomness of such parameters as heat conduction coefficient,heat exchange coefficient,etc, the introduction of which into heat conduction analysis is conductive to more objective and scientific analysis results. Therefore,research on numerical methods for stochastic heat conduction analysis is of great value in both theoretical research and engineering application. Based on taking full advantages of the interface element method(IEM), a new numerical method is developed in this project for stochastic heat conduction analysis based on the coupling of the interface element method and pseudo excitation method. The former can be applied to both continuous and discontinuous field problems. Possible thermal discontinuity in the media can be properly reflected. Compared with other numerical methods, the IEM has such advantages as high accuracy and arbitrary elements. The latter is an accurate and efficient method of random dynamic analysis, the application of which means that stationary random vibration analysis can be transformed into harmonic vibration analysis,and response analysis into deterministic time series analysis for non-stationary random excitation, thereby greatly simplifying the calculation procedure and obtaining high calculation accuracy. Based on taking full advantages of IEM and pseudo excitation method, an accurate and efficient numerical method for stochastic heat conduction analysis can be constructed by further introducing precise integration method and orthogonal expansion method. Implementation process for engineering application of this method is also proposed.The completeness of this project is significant to both theoretical and practical aspects.

由于受工程中许多不确定性因素的影响,导热系数、换热系数和环境温度等参数往往具有随机性。将这些参数的随机性引入热传导分析中会使分析结果更客观、更科学， 因此对随机热传导分析数值方法的研究具有重要的理论研究意义和工程应用价值。本项目将基于界面元法与虚拟激励法相耦合，提出一种新的随机热传导分析数值方法。界面元法适用于连续及不连续温度场，能反映介质可能存在的温度不连续性，较以往数值方法具有精度高、以及适用于任意形状单元的优点。虚拟激励法是一种用于随机振动分析的精确高效的方法。这种方法将平稳随机振动分析转化为简谐振动分析，将非平稳随机振动分析转化为确定性时间历程分析，从而使计算步骤大大简化，却仍保持理论上的精确性。在充分发挥界面元法和虚拟激励法优势的基础上，进一步引入精细积分法与正交展开法,构建一种精确、高效的随机热传导分析方法，并为本方法的工程应用提供实施流程。项目的完成具有重要的理论和实用意义。

由于制造工艺的限制、认知的匮乏、测量的误差以及环境因素的变化，不确定性以多种形式广泛存在于实际工程问题中。传统的确定性分析方法未能定量考虑这些随机因素的影响，经证明不够科学。将导热系数、换热系数和环境温度等参数的随机性引入到热传导分析中会使分析结果更客观、更科学。因此对随机热传导分析数值方法的研究具有重要的理论研究意义和工程应用价值。鉴于界面元离散模型中的块体元可以为任意形状，适用于连续及不连续温度场，能反映介质可能存在的温度不连续性. 较以往数值方法，界面元法具有精度高和基本未知量少的优点，为温度场与位移场、应力场的耦合奠定了基础。虚拟激励法自发表以来，引起了学术界和工程界较大的关注。这种方法将平稳随机振动分析转化为简谐振动分析，将非平稳随机振动分析转化为确定性时间历程分析，进而不仅使计算步骤大大简化，而且能保持理论上的精确性。因此，虚拟激励法能使以往大型复杂的结构受随机激励响应不能用传统方法计算的问题得到较好的解决。本项目基于界面元法和虚拟激励法构建了一种精确、高效的随机热传导分析方法。项目培养了多名青年教师，研究生等人才，发表了多篇学术论文，为国家和社会发展创造了良好的社会经济效益。