两相多孔介质弹塑性动力反应计算分析的显式有限元方法

Explicit Finite Element Method for Calculation and Analysis of the Elasto-plastic Dynamic Response of Fluid-saturated Porous Media

应用连续介质力学的基本原理,针对流体饱和两相多孔介质的特点,建立起增量形式的两相多孔介质弹塑性波动方程组,以实现对两相多孔介质弹塑性动力反应的描述．运用伽辽金方法对该波动方程组进行空间离散,得到两相多孔介质弹塑性波动方程组的伽辽金弱式,并应用中心差分法与Newmark常平均加速度法相结合的时域积分方法,对上述波动方程组进行时间离散,构造求解两相多孔介质弹塑性波动方程组的显式时间积分列式,从而形成流体饱和两相多孔介质弹塑性动力反应计算分析的时域显式有限元方法．该方法采用了解耦技术,不需要求解联立方程组,具有节省计算机内存空间和能够提高计算速度等优点．

In order to describe the elasto-plastic dynamic response of fluid-saturated porous media, incremental elasto-plastic wave equations of fluid-saturated porous media are developed by the fundmental theory of continuum mechanics and in accordunce with the characteristic of fluid-saturated porous media. The above equations are divided in the space domain to get their Galerkin formula, and these formulas are divided in the time domain with the integral method, which consists of the central difference method and the Newmark constant average acceleration method to get the explicit time integral formulas for solving the above wave equations. On the basis of the integral formulas mentioned above, the time-domain explicit finite element method is developed for calculation and analysis of the elasto-plastic dynamic response of fluid-saturated porous media. In this method, the decoupling technique is adopted and it does not need to solve a set of linear equations in each time step, so the compuer memory space can be saved considerably and the calculation speed can be increased sharply by using it.