有限差分法和隐式龙格库塔法求解Burgers方程

提出一个新的方法求解一维Burgers方程,组合使用有限差分法和隐式龙格库塔法求解Burgers方程。首先使用二阶有限差分法进行空间离散,得到一个常微分方程组,然后使用高阶A稳定的隐式龙格库塔法求解常微分方程组,最后比较数值解和精确解,数值结果证实该方法有很高的精度和稳定性。     

Appell方程Mei对称性的新型守恒量

研究完整系统Appell方程的Mei对称性导致的新型守恒量。首先,研究一般无限小变换的Mei对称性;其次,得到系统 Mei 对称性直接导致的守恒量的条件和形式;最后,举例说明结果的应用。     

一类可修复系统的解的存在唯一性

对于一类具有人为故障率,修复率时间任意分布的可修复系统的数学模型,利用泛函理论将此系统转换为Banach空间下的第二型Volterra微分-积分方程,利用泛函分析初等方法得到系统解的存在唯一性证明,并同时得到系统解的形式。     

Hot compressive deformation behavior and constitutive relationship of Al-Zn-Mg-Zr alloy with trace amounts of Sc

Abstract： The hot deformation behaviors of AI-Zn-Mg-Sc-Zr alloy were investigated in a temperature range of 340-500℃ and a strain rate range of 0.001-10 s 1 using uniaxial compression test on Gleeble-1500 thermal simulation machine. The results show that the flow stress increases with increasing strain and tends to be constant after a peak value. The flow stress increases with increasing strain rate and decreases with increasing deformation temperature. The phenomenon of dynamic recovery and dynamic recrystallization can be observed by microstructural evolutions. Based on the hyperbolic Arrhenius-type equation, the true stress-true strain data from the tests were employed to establish the constitutive equation considering the effect of the true strain on material constants （α, β, Q, n and A）, which reveals the dependence of the flow stress on strain, strain rate and deformation temperature. The predicted stress-strain curves are in good agreement with experimental results, which confirms that the developed constitutive equations are suitable to research the hot deformation behaviors of Al-Zn-Mg-Sc-Zr alloy.     

Scattering wave field around a cavity with circular cross-section embedded in saturated soil using boundary element method

Based on Biot＇s theory and considering the properties of a cavity, the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated soil are obtained using integral transform methods. The Cauchy type singularity of the boundary integral equation is discussed. The effectiveness of the properties of soil mass and incident field on the dynamic stress concentration and pore pressure concentration around a cavity is analyzed. Our results are in good agreement with the existing solution. The numerical results of this work show that the dynamic stress concentration and pore pressure concentration are influenced by the degree of fluid-solid coupling as well as the pore compressibility and water permeability of saturated soil. With increased degree of fluid-solid coupling, the dynamic stress concentration improves from 1.87 to 3.42 and the scattering becomes more significant. With decreased index of soil mass compressibility, the dynamic stress concentration increases and its maximum reaches 3.67. The dynamic stress concentration increases from 1.64 to 3.49 and pore pressure concentration improves from 0.18 to 0.46 with decreased water permeability of saturated soil.     

气体钻井钻柱损伤疲劳寿命预测模型研究

针对气体钻井钻柱频繁断裂失效问题,以现代损伤力学研究为基础,分析钻柱损伤演化过程,建立气体钻井钻柱损伤疲劳寿命预测模型。由钻柱损伤疲劳寿命模型得出损伤度是影响钻柱疲劳寿命的主要因素,引入损伤梯度并进一步通过算例研究钻柱所受轴向载荷、损伤度及应变之间的关系。根据理论与算例分析可得,随着轴向载荷增大,损伤度与应变逐步由空间周期关系转变为类周期关系,出现损伤局部化,导致钻柱的疲劳失效。     

适合可渗海床上波浪传播的高阶Boussinesq方程

为在数学模型中考虑渗透性介质对波浪传播的影响,在多孔介质流体运动方程中引入拖曳阻力和惯性力,引出Laplace方程和边界条件.对控制方程无因次化,并以自由表面处速度势和交界面上的速度势进行幂级展开,推导了以静止水平面上速度、交界面上速度和波面升高3个变量表达的Boussinesq方程.给出积分平均速度或任一水深处速度与以上2个速度之间的关系式,进而推导出另外2个Boussinesq方程,并通过引入高阶色散项对方程进行加强以拓展其适用水深.对方程进行了理论分析,将相速度及衰减率与解析解进行了比较,发现四阶色散性方程具有最佳精度.不考虑渗透影响时,在2%误差下,四阶方程可适用最大无因次水深达到5.82.该高阶Boussinesq方程不仅可用于研究渗透海床上波浪的传播变形,也适用非渗透海床上的深水波浪传播变形.     

抛物线型有损传输线频域灵敏度分析的伴随方程法

提出了一种求解含抛物线型有损非均匀线网络频域灵敏度的方法。该方法首先将抛物线型有损非均匀线用科罗达(Kuroda)等效方法变换成有损均匀线及若干集中元件组成的等效电路,然后借助伴随网络方程法求出抛物线型有损非均匀传输线等参数的频域灵敏度。给出了计算实例,并通过扰动法进行了验证。