A New Hybrid Stress Element with Fluid

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.