非线性晃动问题的 ALE 边界元方法

THE ALE BOUNDARY ELEMENT METHODS IN SOLVING NONLINEAR SHOSHING PROBLEMS

利用ＡＬＥ（任意的Ｌａｇｒａｎｇｅ－Ｅｕｌｅｒ）边界元方法数值求解了具有自由液面的非线性晃动问题，即受外力激励下流体的非线性振动问题。把ＡＬＥ有限元方法的思想应用到边界元方法中，得到了ＡＬＥ边界元方法。对于自由液面的非线性动力边界条件，应用Ｇａｌｅｒｋｉｎ加权方法进行了有限元数值离散。为了增加求解精度，对动力边界条件提出了增加误差修正项的数值求解方法。对时间变量采用Ｎｅｗｍａｒｋ方法进行离散。推导了系统非线性方程的预测－多次校正法迭代格式。进行了算例分析与比较，得到了令人比较满意的结果。

The ALE(Arbitrary Lagrange Euler)boundary element method is used for dealing with nonlinear sloshing problem(nonlinear oscillations of a liquid in a container subjected to forced oscillation) The ALE boundary element methods is derived by applying the idea of ALE finite element method The dynamic boundary condition is redused to a weighted residual equation by employing the Galerkin nethod Due to the nonlinearity of the problem,a general corrective procedure is used for the numerical analysis The system equation is discretized by the use of Newmark Method timewise and the predict multi corrective steps method is used in iteration procedure At last,computation example and computed result is given