【作者】 李晖敏；

【导师】 何天虎；

【作者基本信息】 兰州理工大学 ， 工程力学， 2013， 硕士

【摘要】 经典的热弹性理论,包括非耦合及耦合的热弹性理论,由于其热传导方程是扩散型的,决定了热在弹性介质中以无限大的速度进行传播,这意味着当弹性介质受到热扰动作用时,这种扰动效应将瞬间传播到无限远处,这有违于物理常识且与实验观测相悖。为了弥补经典热弹性理论的不足,学者们相继发展了广义的热弹性理论。目前,应用较为广泛的广义热弹性理论主要有由Lord和Shulman提出的L-S理论,及Green和Lindsay提出的G-L理论。这两种理论都能描述热以有限速度在弹性介质中进行传播的波动效应及弹性场和温度场间的耦合效应。扩散现象是指物质分子从高浓度区域向低浓度区域自由迁移直到均匀分布的现象。通常,扩散过程是由Fick定律来描述的,但Fick定律形式单一,没有考虑扩散物与基体及温度间的相互作用。Nowaski于1974年提出了耦合的热-弹-扩散理论,该理论考虑了变形场与扩散场间的耦合效应,但所描述的热弹波及扩散波的传播速度为无限大。最近,Sherief等在L-S广义热弹性理论和Fick定律的基础上,发展得到了广义的热-弹-扩散理论。该理论不但能描述变形场、温度场和扩散场间的耦合效应,而且能描述变形场、温度场和扩散场以波的形式并以有限的速度进行传输。本论文基于广义热弹性理论和广义热弹性扩散理论,开展了如下的研究工作：(1)L-S理论下材料特性参数随温度变化的广义热弹耦合问题的动态响应；(2)广义热弹扩散耦合问题的动态响应。这些问题由于属多场耦合问题,解析求解几乎是不可能的,通常采用数值方法进行求解,如积分变换及其数值反变换法及有限单元法。文中给出了各个问题的控制方程,及相应的虚位移原理,并推导得到了相应的有限元控制方程。对有限元方程在时间域中直接进行了求解,避免了利用积分变换法求解此类耦合问题时,由于离散误差和截断误差而引起的计算精度降低的问题。文中以铜质材料半无限大体为计算模型,数值得到了半无限大体中的温度、位移、应力等物理量的分布规律,并重点研究了随温度变化的材料特性参数对各物理量的影响效应。计算结果表明,在研究多场耦合问题时,考虑材料特性参数随温度的变化效应,对复杂服役环境中的结构的功能性设计和安全性设计,都具有重要的理论和现实意义。更多还原

【Abstract】 In classical uncoupled or coupled thermoelastic theory, the heat conduction equation is of diffusion type, which leads to heat propagating in elastic media with infinite speed. This means if an elastic medium is subjected to a heat disturbance, the effect of the disturbance will be felt instantaneously at distance far from the disturbance, which is physically impossible and contrary to experimental observations. To amend the inherent paradox in classical thermoelastic theories, the generalized thermoelastic theories were developed subsequently. At present, there are two extensively adopted generalized thermoelastic theories:one was put forth by Lord and Shulman (L-S) and the other by Green and Lindsay (G-L). Both theories can describe heat propagating in elastic media as a wave with finite speed and the coupling effect between deformation field and temperature field.Diffusion can be defined as the random walk of material particles from regions of high concentration to regions of lower concentration. Normally, diffusion process is modeled by Fick’s law. Nevertheless, Fick’s law is too simple to take into consideration the mutual interplay between the introduced substance and the substrate or the effect of temperature on the interplay. In1974, Nowaski put forward the theory of thermoelastic diffusion in which the coupling effect between the deformation field and the diffusion field was considered while infinite propagating speed of thermoelastic wave as well as diffusive wave was predicted. Recently, Sherief et al. proposed the generalized thermoelastic diffusion theory based on L-S theory and Fick’s law. This theory can describe not only the finite speed of deformation field, temperature field as well as diffusion field propagation as a wave respectively, but also the coupling effects among these three fields.In this thesis, the generalized thermoelastidc theories and the generalized thermoelastic diffusion theory are applied to dealing with the following problems:(1) the dynamic response of generalized thermoelastic coupled problem with temperature-dependent properties in the context of L-S theory;(2) the dynamic response of generalized thermoelastic diffusive problem. All these problems are multi-fields coupled, and it is barely possible to get their solutions analytically. Alternatively, numerical method, such as integral transform as well as its numerical inversion and finite element method etc., is commonly adopted to solve such problems. In this thesis, the governing equations for each problem are formulated and the corresponding virtual displacement principles are given. The corresponding finite element equations are obtained by means of virtual displacement principle. To avoid loss of calculation precision caused by discrete error and truncation error in the method of integral transform, the obtained finite element equations are solved directly in time domain. To carry out the calculation, a thin slim strip made of copper is set as the calculating model. The variations of the considered quantities such as temperature, displacement and stress etc. are obtained numerically. In calculation, the emphasis is put on examining the effect of temperature-dependent properties on the considered quantities. The results show that taking the temperature-dependence properties into account in the investigation of multi-fields problems has very important theoretical and practical meanings, especially, in the design of function and safety of structures serving in complex environment.更多还原