ALE有限元方法在金属塑性加工中的应用

摘要

In the ALE formulation, the mesh, which is generated in the reference configuration, is dependent of the material and space. So, unlike the Lagrangian formulation, ALE finite element can't cause the entanglement and degeneration of the mesh, and can describe accurately the free surface of the material during the processes, which is impossible in the Eulerian FEM. The paper makes use of the ALE formulation to simulation numerically the plastic deforming, and derives the final equations of ALE finite elements method. At last the example shows its effectiveness.%ALE (Arbitrary Lagrangian-Eulerian)有限元方法中，网格划分是在参考构形中进行的，网格独立于物体和空间运动，可以根据需要自由选取。因此，ALE有限元避免了Lagrangian有限元中的网格畸变，又克服了Eulerian有限元中难以描述自由边界的不足。对ALE有限元用于分析塑性加工过程进行了探讨，并利用Galerkin方法，推导了离散形式的求解方程。最后的数值算例验证了该算法的有效性。