几种非均匀应变有限单元的最大特征频率和稳定的时间步距

MAXIMUM CHARACTERISTIC FREQUENCIES OF SEVERAL NONUNIFORM STRAIN ELEMENTS AND STABLE TIME STEPS

通过多点高斯积分研究了非均匀应变有限单元的最大特征频率 ,给出了单相和两相介质若干简单、非均匀应变有限单元最大特征频率上界的计算公式 ,扩充了Flanagan的研究结果 .由此 ,给出了几种显式积分格式的实用稳定性条件 .并通过两相介质的算例 ,检验了该稳定性条件 .

Considering that the stability results obtained by modal method depend on system maximum characteristic frequency are impractical, the element maximum characteristic frequencies, proved to be the upper bounds of the system frequency, are evaluated in the case of multi-point Gauss integral. Combining the modal method results, some new practical stability conditions are proposed, which complement Flanagan's results in uniform strain case. The new stability conditions are tested to be reasonable through a numerical example of two-phase media.