DIFFERENTIAL-ALGEBRAIC APPROACH TO COUPLED PROBLEMS OF DYNAMIC THERMOELASTICITY

An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.     

复杂结构热屈曲有限元分析

实现了机械载荷和温度载荷共同作用下复杂结构的弹性分歧热屈曲有限元分析，计算结果表明，局部温度场将使结构的屈曲强度大幅度降低。复杂结构的热屈曲研究具有理论和实际意义。本文研究成果表明，从计算结构力学角度出发，探讨强热源作用复杂结构引起宏观破坏机理研究的可行性     

双材料板条的界面应力问题——温度沿板厚呈线性分布的情况

本文给出双材料板条结构的Ｓｕｈｉｒ界面应力微分方程一般解，进而求解了温度沿板呈线性分时因异材料失配引起的界面剪应力和剥离应力。此解包含了均匀升温情况下的Ｓｕｈｉｒ解。     

高超音速湍流分离表面热流率的脉动特性

本文给出高超音速湍流分离不稳定特性的实验研究结果。试验条件是:自由流马赫数为 7.8,单位长度雷诺数为 3.5×10~7/米。分离流场由有限展长前向台阶产生,并用有高空间分辨率和快速响应的一列平齐安装的铂膜电阻温度计和多通道系统测量其表面热流率脉动。信号的条件采样分析结果表明:分离激波的根部由一束压缩波构成,流向展长约二分之一来流边界层厚度,在边界层外汇聚成单一主激波。这种激波结构极其不稳定,出现大尺度运动,流向运动的尺度约为分离激波上游影响区域长度的22％。激波振荡频率为一宽频带,主要集中在 1～3 千赫。在分离激波运动区域,热流脉动呈间歇性,在无扰动和激波扰动间跳跃。可以认为这种间歇性是分离激波系统大尺度振荡的结果。在激波运动区域的下游为分离区,流体继续压缩,热流脉动无间歇。     

板的非线性热弹耦合振动（Ⅰ）：近似解析解

本文以文[2,3,4]为基础,导出了板的热弹耦合非线性振动控制方程,在采用Galerkin法离散化以后,按各个变量性质分别用多尺度法或正则摄动法求得近似解析解。籍此可揭示系统各参数对非线性热弹耦合振动影响的机理和作出必要的近似计算,对工程实际具有较大的参考价值。     

热/机械载荷下功能梯度材料矩形厚板的弯曲行为

采用Reddy高阶剪切板理论，考虑材料物性参数随坐标和温度变化的特性，研究在均匀变化的温度场内功能梯度材料矩形板在面内与横向载荷共同作用下的横向弯曲问题，基于一维DQ法和Galerkin技术，给出了一对边固支，另对边任意约束时板弯曲问题的半解析解，以Si3N4/SUS304板为例考察了材料组份，温度场，面内载荷及边界约束条件等对功能梯度材料板弯曲行为的影响。     

Thermoelastic stresses in SiC single crystals grown by the physical vapor transport method

A finite element-based thermoelastic anisotropic stress model for hexagonal silicon carbide polytype is developed for the calculation of thermal stresses in SiC crystals grown by the physical vapor transport method. The composite structure of the growing SiC crystal and graphite lid is considered in the model. The thermal expansion match between the crucible lid and SiC crystal is studied for the first time. The influence of thermal stress on the dislocation density and crystal quality is discussed. The project supported by the National Natural Science Foundation of China (10472126) and the Knowledge Innovation Program of Chinese Academy of Sciences. The English text was polished by Keren Wang     

热压电变分原理

热释电介的许多传感器及机敏结构或中的关键材料，本文系统地讨论了在基础理论和数值计算中极具重要地位的各类变分原理，包括准静态变分原理、动态变分原理和关于固有频率的变分原理。最后建立了关于静态压电要板的变分原理，并由此导出了各向异性压电板的控制方程及边界条件。     

耦合热弹性问题的分区变分原理及其广义变分原理

本文在文献[1]和[2]的基础上建立并论证了耦合热弹性问题的分区变分原理及其分区广义变分原理     

UPWIND LOCAL DIFFERENTIAL QUADRATURE METHOD FOR SOLVING COUPLED VISCOUS FLOW AND HEAT TRANSFER EQUATIONS

The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method. A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region. For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction, the satisfactory numerical solutions were obtained by using ULDQM with a few grid points. The numerical results show that the ULDQM possesses advantages including well convergence, less computational workload and storage as compared with the low-order finite difference method.