2.5D有限元建模关键问题——边界条件、网格划分及计算域选取

Key issues in modeling process of 2.5D finite element method——boundary conditions,meshing and computing range selection

为了提高2.5D有限元数值计算的求解精度及建模效率,分析了移动荷载作用下地基系统的动力响应特点,确定了计算域选取及网格划分的基本规则,评价了地基分层对波场的影响及边界的波动吸收效果,提出了可以规避边界影响的建模思路。分析结果表明:当计算域尺寸满足低频振动要求(约60 m)时,反射波对计算结果的影响可以忽略;建模时可以采用辐射状网格划分,最小网格尺寸需满足高频振动要求(约0.5-1.0 m)。荷载运行速度小于地基瑞利波速时没有波动传播现象,建议直接采用固定边界;荷载运行速度大于地基瑞利波速时可以通过切取局部计算域的方式规避反射波的影响,此时计算域半宽和纵向空间范围的选取需要遵循与马赫锥锥角和列车全长相关的几何关系。荷载影响深度内的地基分层会扰乱地基波场,当地基上覆软弱土层或软弱夹层时,波动会在软土层聚集并在加载点后形成多个马赫锥。

In order to improve the solution accuracy and modeling efficiency of 2.5 D finite element numerical method,the dynamic response characteristics of ground system under moving load are addressed.The basic rules in selecting computing range and meshing are established.Moreover,the effects of ground stratification on the wave field and wave absorption capacity of boundaries are evaluated.Finally,the modeling approach which can avoid the effect of boundary strictly is suggested.The results indicate that the effect of reflection wave on the results can be overlooked once the computing range fits the requirement of low frequency vibration(about 60 m),and radial mesh can be used in modeling and the minimum mesh size should meet the requirement of high frequency vibration(about 0.5-1.0 m).There is no wave propagation when the moving speed of load is lower than the Rayleigh wave velocity of ground and the fixed boundary is suggested.In addition,the influence of reflected wave can be completely avoided by cutting the local computation range when the moving speed of load is higher than the Rayleigh wave velocity of ground.In that condition,the half-width and longitudinal space range of model should be confirmed following the geometric relation related to the Mach cone angle and the full length of the train.Furthermore,the layered interface at the load influence depth will disturb the wave filed of ground.Wave will accumulate in the soft soil and multiple Mach cones will occur after the loading point when the ground is covered with soft soil or soft interlayer.