基于六面体覆盖的三维数值流形方法的理论探讨与应用

介绍了基于六面体单元的三维数值流形方法的基本理论，并在六面体单元中采用了有限元中C8型等参单元的形函数作为流形元中的覆盖函数。推导了相应平衡方程的刚度、初始应力、点荷载、体荷载、惯性力、固定点、法向接触、切向接触和摩擦力子矩阵。在二维接触中，切向应力和摩擦力的方向很容易沿着接触边得到，但在三维问题中要在接触面上确定该方向则非常困难，这也是所有计算方法在遇到三维接触时的难题。引入了向量理论和迭代方法，避开了相应困难的干扰。最后，给出了一个简单的地下失稳算例，证明了该三维方法的正确性。

APPLICATION AND DISCUSSION OF THREE DIMENSIONAL NUMERICAL MANIFOLD METHOD BASED ON HEXAHEDRON ELEMENT

In this paper,three-dimensional numerical manifold method (NMM) based on hexahedron element is proposed and the shape functions of C8 isoparametric element are used as the cover weight functions. All sub-matrices of equilibrium equations are derived according to this cover weight function. In 2D contact,the direction of shear stiffness and friction force is easily defined along the contact edge. For the corresponding 3D contact problem,it is difficult to determine similar relations in simple way. In the present paper,vector theory and iterative method are proposed to overcome this kind of difficulty. An example of underground excavation is also presented.