无限长圆柱非稳态导热集总参数法应用

圆柱体进行非稳态导热时,集总参数法只适用于Bi〈1的情况,Bi〉1时一般采用根据解析解绘制的Heisler图线．由于前者适用范围窄,后者误差大,探讨一个非稳态导热的实用便捷公式具有重要意义．以无限长圆柱为例,研究在0〈Bi〈∞条件下非稳态导热平均温度集总参数分析方法,定义必要的参数,建立了平均温度瞬态响应关系式．拓展了传统的非稳态导热集总参数法应用范围．数值分析给出了计算关系式的辅助参数表．通过推导出的公式,结合参数表来计算工程实际问题,比通用的Heisler图解法更为简洁方便．     

无限大平板非稳态导热过程的数字特征

对无限大平板非稳态导热过程的平均温度和耗散函数这2个数字特征进行了研究。得到了对流换热边界条件下无量纲平均过余温度的数学模型;分析了表面温度系数随特征值与毕渥数的变化规律;定义了相应的时间常数,它是衡量无量纲平均过余温度衰减速率快慢的指标;并对毕渥数取极限时无量纲平均过余温度的变化规律做了讨论。利用格林公式推导出了热势与耗散函数之间的关系,并与机械能耗散系统进行了相似性分析。得到了对流换热边界条件下耗散函数随时间的变化规律,并将其与平均过余温度的变化规律做了比较。     

复合球体非稳态导热的理论解及实例分析

针对二层复合球体在第三类边界条件下的导热微分方程进行了分析求解．以法国Cristopia公司的C．00型蓄冷冰球为例,对温度函数进行求解,分析了温度函数中特征值、指数值的变化规律．当水分别处于固态和液态时,画出了3个典型时刻冰和水的温度曲线．结果表明,在相同的表面传热条件下,冰和水的最外层几乎同时达到0℃．冰内温度变化比水内变化更剧烈,水开始结冰比冰开始融化需要更长的时间．提供的理论解可用于对相关导热问题的求解,以及为近似解或数值解的准确性提供检验标准．     

用稳态平板法测定不良导体导热系数的实验研究

本对不良导体导热系数的测量作了研究。主要从该实验的测量装置,测量条件和测量方法上作了改进,取得了较满意的结果。     

关于不稳态导热集总系统的判定

本文对不稳态导热集总系统的判定问题进行了分析和计算,从而对判定中的误解和混乱进行了澄清。     

液晶屏非稳态温度响应特性的理论分析

为保证有源液晶显示器能在低温环境和温度变化较快的情况下可靠地工作,必须掌握器件内部温度场的分布及其对迅变温度的动态响应,以便提供间接测量器件内部温度的理论依据。通过经典解析法求解得到了内部温度分布和动态响应,并用温度传感器去测试阶跃响应,其响应曲线与经典解析法的解相符。上述２种结果表明液晶屏后表面上的温度在动态情况下要滞后环境温度４３ｓ。故其后表面温度不能及时地反映环境温度的变化。     

第三类边界条件下二维非稳态导热的分析解

文本给出了第三类边界条件下矩形长方体、短圆柱非稳态导热的分析解。解的获得是采用分离变量法解导热微分方程式的方法。分析解的结果证明了多维非稳态导热解的乘积法则。     

混凝土非稳态温度场的计算

对混凝土受高温作用时温度场的计算进行了分析研究,给非稳态导热微分方程设计了合适的计算方法,此方法与通常采用的有限单元法结合差分法相比,具有计算简单、稳定性好、步长选择灵活和应用方便等特点,得到的结果与实验数据吻合良好．实验数据具有不同的混凝土截面、不同的最高设计温度以及温度场中不同的点位．     

拉普拉斯变换法在非稳态导热中的应用

非稳态导热问题的数学模型为偏微分方程组。给出了利用拉普拉斯变换法求解非稳态导熟问题的方法步骤,并采用此方法对边界条件为恒定热流和变热流两种情况进行了求解。     

一种二维非稳态导热问题的数值解法

在采用当量第三类边界条件基础上，依据交替方向隐式（ADI）法，导出了适合于三类边界条件的二维非稳态导热问题的差分方程式．这些方程式及相应的程序为类似的传热问题的求解提供了方便．     

非稳态导热初值问题稳定性条件的分析

从非稳态导热的离散方程出发，根据Von Neumann的格式稳定性判别方法，给出二维导热数值计算显式格式的稳定性条件。由统计热力学的观点对稳定性条件进行分析，认为稳定性条件实际上是物质本身的热容量对数值计算的一种限制。     

Fractal analysis of thermal conduction of loose coal

For deep mining engineering,heat transfer of coal mass is a vital factor in the thermal environment of coal mines.In order to study the thermal conduction mechanism,we obtained gray images of coal mass microstructure by scanning samples with a digital microscope.With the use of Matlab,these gray images were transformed into binary images,which were then transformed into a corresponding matrix consisting only of the values 0 and 1.According to the calculation method of box-counting dimension,we calculated the fractal dimension of the loose coal to be approximately 1.86.The thermal conductivity expressions of loose coal were derived based on the simulation method of thermal resistance.We calculated the thermal conductivity of loose coal by using a fractal model and compared the calculated values with our experimental data.The results show that the test data show an encouraging agreement with the calculated values.Hence fractal theory is a feasible method for studying thermal conductivity of loose coal.     

自由 固定边界板的导波

针对平面应变弹性波动问题，研究了自由-固定边界无限大弹性板中P-SV波的传播特性.基于特征方程式，理论上求得了截止频率，并与自由-自由边界无限大弹性板的截止频率作了比较.在短波区域，理论上求得最低区的弥散曲线分支的极限相速度为Rayleigh波的波速，而其他区的弥散曲线分支的极限相速度为剪切波的波速.通过数值计算给出了弥散曲线的前十个分支.计算结果表明，在长波区域，第二和第四分支的群速度小于零；在短波区域，只有第二分支的相速度趋近于Rayleigh波的波速.     

Theoretical analysis of thermal/electric-filed poling silica glass

Based on the experimental results, three basic conclusions are summarized for the thermal/electric-field poling (TEFP) silica materials, with which the second-order nonlinear optical coefficient in the bulk silica glass after TEFP is calculated, and relationships between the coefficient and the applied voltage V0 in the poling process and the thickness of the nonlinear layer created from the poling are obtained. Theoretical results show that the second-order susceptibility x(2) and the second-harmonic efficiency η in the poled bulk glass are proportional to (?) and V02,respectively; x(2)-0.2-1.6 pm/v for the bulk glass after the typical TEFP; x(2) decreases with an increase in the poling time after the TEFP silica glass approximately reaches the steady state. Theoretical results are well consistent with the experimental reports.     

碳纤维板加固梁的理论计算与试验分析

通过计算内嵌碳纤维增强复含材料（CFRP）抗弯加固钢筋混凝土构件开裂时的开裂荷载和受拉钢筋屈服时的屈服荷载,并对加固梁和对比梁进行了静力加载试验,结果表明该计算结果和试验基本吻合,可以用来分析碳纤维板加固梁的效果。混凝土梁经碳纤维板加固后,开裂荷载和屈服荷载都有一定程度的提高,内嵌碳纤维板能提高梁的极限承载力,是一种有效的加固方法。     

无限大板椭圆孔的分支裂纹的边界元分析

采用常位移不连续单元和裂尖位移不连续单元构成的边界元方法研究内部压力作用下无限大板中源于椭圆孔的分支裂纹.在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其他边界.结果表明,该数值方法对计算无限大板中复杂裂纹的应力强度因子是有效的,可以揭示裂纹体几何对应力强度因子的影响.     

Elastoplastic analysis for infinite plate with centric crack loaded by two pairs of point shear forces

The near crack line analysis method was used to investigate a crack loaded by two pairs of point shear forces in an infinite plate in an elastic-perfectly plastic solid, and the analytical solution was obtained. The solutions include: the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near crack line, law that the length of the plastic zone along the crack line is varied with an external loads, and the bearing capacity of an infinite plate with a center crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been made and no other assumption have been taken.     

Elastoplastic analysis for infinite plate with centric crack loaded by two pairs of point shear forces

The near crack line analysis method was used to investigate a crack loaded by two pairs of point shear forces in an infinite plate in an elastic-perfectly plastic solid, and the analytical solution was obtained. The solutions include: the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near crack line, law that the length of the plastic zone along the crack line is varied with an external loads, and the bearing capacity of an infinite plate with a center crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been made and no other assumption have been taken.     

理想结合两层无限大弹性板中波的传播

针对理想结合的两层无限大弹性板，研究了Lamb波的传播特性.从基本特征方程式出发，理论上导出了两组非耦合的求解截止频率的方程式；利用泰勒展开技术，给出了长波区域弯曲振动模式和伸缩振动模式的弥散曲线渐近表达式；利用行列式运算规则，得到了弥散曲线在短波区域的渐近行为.数值计算表明，两层无限大弹性板频谱曲线图上存在且只有两个分支通过原点；在相速度谱曲线上，长波区域存在且只有一个极限相速度，在短波区域有两条分支分别趋近于两种板的Rayleigh波波速.     

移动荷载作用下饱和土地基无限板的动力响应

利用Biot波动理论、无限大板的弹性理论,研究了移动荷载作用下饱和土地基上覆弹性板的动力响应问题.首先引入两类势函数解耦Biot波动方程,由所引入势函数及二维Fourier变换,得出了土体位移、应力及孔压在变换域内的通解.再根据无限大板的弹性理论求解变换域内饱和土的波动系数及板的内力表达式.最后利用IFFT算法得出时间-空间域内的解析解.通过具体算例,分析了荷载移动速度、土层剪切模量对板内力、土体的动力响应的影响.