引用本文: 尉亚军, 吴华, 徐成辉等. 连续介质力学的类比思维教学法：黏弹性力学vs.广义热传导. 力学与实践, xxxx, x(x): 1-6.
Yu Yajun, Wu Hua, Xu Chenghui, et al. Analogical thinking pedagogy for continuum mechanics: viscoelastic mechanics versus generalized heat transfer. Mechanics in Engineering, xxxx, x(x): 1-6.
 Citation: Yu Yajun, Wu Hua, Xu Chenghui, et al. Analogical thinking pedagogy for continuum mechanics: viscoelastic mechanics versus generalized heat transfer. Mechanics in Engineering, xxxx, x(x): 1-6.

ANALOGICAL THINKING PEDAGOGY FOR CONTINUUM MECHANICS: VISCOELASTIC MECHANICS VERSUS GENERALIZED HEAT TRANSFER

• 摘要: 类比是重要创新思维方式，发挥类比思维教育价值，强化学生类比思维训练，有助于创新人才培养。本文以黏弹性力学和广义热传导教学模块为抓手，展现类比思维教学法在连续介质力学课程运用的设计案例。首先，基于力学弹性单元和黏性单元，采用串并联方法，推导黏弹性力学Maxwell模型和Kelvin-Voigt模型。其次，给出广义热传导Cattaneo-Vernotte模型和Green-Naghdi模型，介绍Green-Naghdi模型热位移概念的起源。随后，通过类比方法引入热学“弹性”单元和“黏性”单元，运用串并联方法实现Cattaneo-Vernotte模型和Green-Naghdi模型的重构，澄清黏弹性力学和广义热传导各模型间的对应类比关系。最后，分析热学基本方程与力学基本方程的差异，指出对研究对象间差异性的关注，也是基于类比方法启发创新思维的重要手段。

Abstract: Analogy is an important innovative thought. Utilizing educational value of analogy thought, and strengthening students' analogy thought training are helpful to the cultivation of innovative talents. In this paper, viscoelastic mechanics and generalized heat conduction are used to show design case of analogy thought teaching used in continuum mechanics. Firstly, based on elastic unit and viscous unit of mechanics, the series-parallel method is used to derive the viscoelastic Maxwell model and Kelvin-Voigt model. Secondly, the generalized heat transfer Cattaneo-Vernotte model and Green-Naghdi model are given, and the origin of the concept of thermal displacement in Green-Naghdi model is introduced. Subsequently, "elastic" and "viscous" units of thermal science are introduced by analogy, series-parallel method is applied to realize the reconstruction of Cattaneo-Vernotte model and Green-Naghdi model, and the analogy relationship between viscoelastic mechanics and generalized heat conduction is clarified. Finally, the differences between fundamental equations of thermal science and mechanics are analyzed, and it is pointed out that attention to the differences between research objects is the important approach of creative analogical thinking.

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