In the process of shale gas exploitation, there exits two difficult problems: one is the real numerical simulation of a tremendous number of holes in actual shale; the other is the fluid–solid coupling problem involved in holes, where the difficulty of transition at the interface between the Eulerian grid and the Lagrangian grid becomes the most important. In response to these two problems, this paper establishes an element model with both fluid and solid. At the fluid–solid interface, the equilibrium condition of the surface force is introduced to obtain the modified complementary energy functional, and a new hybrid stress element with fluid is derived. The comparison of the simulation results with those of the ordinary commercial finite element software verifies the effectiveness and efficiency of this element, and proves its applicability in the problem of shale with numerous holes. Furthermore, this element can be extended to general problems of solid with fluid in.

在页岩气开发过程中，存在两个难题：一是实际页岩中大量孔洞的真实数值模拟；另一个是孔中涉及的流固耦合问题，其中欧拉网格和拉格朗日网格之间的界面过渡困难成为最重要的问题。针对这两个问题，本文建立了流体和固体相结合的单元模型。在流固界面，引入表面力的平衡条件，得到修正的互补能量泛函，推导出一种新的流体混合应力元。仿真结果与普通商用有限元软件的比较验证了该单元的有效性和效率，并证明了其在多孔页岩问题中的适用性。此外，这个元素可以扩展到固体与流体的一般问题。