基于有限单元法的液体晃荡数值模拟

摘要

利用位移格式的有限单元法研究液体晃荡行为.对二维刚性边界条件和三维弹性边界条件矩形储液容器液体晃荡进行分析.得到液体晃荡固有频率、自由液面瞬时高度和自由液面高度时间历程曲线等.二维刚性边界条件的结果与线性解析解具有很好的一致性,验证了有限单元法的适用性.在弹性边界条件下给出了自由液面瞬时高度、自由液面高度时间历程曲线和弹性容器的等效应力,反映了液体晃荡对弹性容器的影响.突出了基于位移格式的有限单元法在处理弹性边界条件液体晃荡问题的优势.%The sloshing waves are analyzed using the displacement-based fluid finite element method.Two kinds of tanks are analyzed with one two dimensional rigid boundary conditions and the other 3D elastic boundary conditions.The sloshing frequency,free surface instantaneous elevation and time history of free surface elevation are obtained.The results of the rigid tank are found to be in good agreement with the linear analytical solutions .which verifies the feasibility of FE method.Free surface instantaneous elevation,time history of free surface elevation and the equivalent stresses in the elastic tank are obtained to give the influence of the sloshing waves on the tank.lt mainly shows the advantage of the displacement-based fluid finite element method in dealing with the sloshing wave s problem with elastic boundary condition.