高阶能量一致积分方法及其在结构动力分析中的应用

能量一致积分方法是一种二阶精度、无条件稳定的逐步积分方法。为提高计算精度,将辛Runge-Kutta方法进行改进,构造出高阶能量一致积分方法一般形式。这种方法既保持了四阶精度,又具有能量一致属性。通过非线性弹性算例验证了方法的精度和数值稳定属性。将方法应用到桁架单元,推导了具体计算格式,并完成对应的非线性计算程序。程序集成了二阶与四阶能量一致积分方法、平均加速度方法(average acceleration method,AAM)以及由AAM构造的四阶方法。通过弹性摆与平面桁架结构非线性动力分析,对比4种逐步积分方法。分析结果表明,四阶能量一致积分方法在精度、稳定性与计算效率上优于其他3种方法。

基于桁架单元的能量一致积分方法

基于能量平衡理论,提出针对桁架单元的能量一致积分方法。该方法具有非线性无条件稳定性,2阶精度。利用中值定理证明算法参数的存在性,并给出参数的求解形式。对离散后的动力方程线性化得到用于迭代的等效刚度矩阵。实现新算法在非线性有限元程序中的嵌入,并以此为基础完成单摆、输电塔体结构的非线性动力分析。数值结果表明,经典的平均加速度方法与隐式中点方法均会表现出能量不一致现象,甚至会产生发散结果;相比而言,该文方法在不同的时间步长情况下都表现出良好的数值稳定性。

Flow Field Around Rushton Turbine in Stirred Tank by Particle Image Velocimetry Measurement

In this paper, particle image velocimetry (PIV) was used to measure the mean and root meansquare(RMS) velocity in the stirred tank with six-flat blade Rushton turbine and with no baffles. Two typesof motion patterns were studied. One was that the impeller runs at constant speed, the other was that the impellerruns at time-dependent speed and in a periodic way. The emphasis of the paper was on the comparison of meanand RMS velocity vector maps and profiles between these two types of motion patterns, and especial attention waspaid to the comparison of the mean velocity, time-averaged RMS velocity, phase averaged RMS velocity betweenthe constant 3 RPS (revolution per second) and time-dependent operation. The Reynolds number was between 763and 1527. The study explained the mechanism that time-dependent RPS is more efficient for mixing than that ofconstant RPS.