Membrane structure is one of the most rapid new spatial structure for modern development, because the membrane material quality is light and firm, wear-resisting, the structure mainly withstands the tension, makes the material performance to be given full play, but also has the following several advantageous factors: (1) The light weight, allows crosses the large space and designs the various shapes; (2) The construction period is short, Easy maintenance, low cost, (3) can meet the requirements of various uses, easy to integrate with the natural environment, by the international construction industry as the 21st century architecture.

The design of membrane structure can be divided into three steps: (1) Finding an initial equilibrium shape and (2) mechanical analysis under various load combinations to ensure safety; (3) cutting production. Developed countries from the 60 's beginning to propose a variety of computational methods, so far by the finite element method for the most advanced, most commonly used methods. The element type is a triangular plane constant strain unit, which is transplanted from the large deformation theory of rigid plate and shell. It can be seen from this paper that the membrane structure is not suitable for using this kind of planar element as only the tensile soft shell. Because for the rigid shell, this kind of plate element can be regarded as the combination of plane stress element and plate bending unit, and the unit rigid array can be formed by merging these two kinds of cells. The membrane structure as a soft shell can not be bending, only by the curvature of the film surface changes, resulting in the film surface internal force redistribution to resist perpendicular to the surface of the load. If the plate element with only plane internal stress is used, then the linear part of the strain will not reflect the influence of the z-direction displacement, which causes the unit to not contain the Z-directional nodal force, and the static is unbalanced for each unit. Fortunately, the nonlinear part of the strain takes into account the effect of z-direction displacement, so that the total equilibrium equation of each unit can be approximately balanced by iteration, the disadvantage is that the displacement of the plane is too much to meet the requirement of balance, and the actual situation is that the displacement and curvature of the plane can only be changed.

Considering these, in this paper, the curved mask element is used for the first time, the linear part of the strain is introduced into the z-direction displacement and the element's curvature and torsion rate, and the nonlinear part still retains the influence term of the z-direction displacement. In this way, the equilibrium equations of each unit or unit can be easily satisfied, the number of iterations is greatly reduced, and the deformation result is more realistic. And because the stress of each point in the unit is different, it is more accurate to judge whether the crease appears. Finally, the curvature and torsion of each element can provide a lot of useful information for judging the correctness and disadvantage of the initial shape finding and cutting down the material.