Most origamis are composed of triangular and quadrilateral facets. Since creases are practically straight, facets can be modelled as 3-node triangles (T3) and 4-node quadrilaterals (Q4) with translational nodal dofs only. While bending is not possible in T3, a corotational consideration is employed to quantify the bending deformation in Q4 under large displacement/rotation but small strain/curvature. The pertinent tangential stiffness matrix turns out to be a simple constant matrix. Meanwhile, the fold angle of the crease is computed by the dot product of two vectors connecting the crease and nodes defining the adjacent facets. Derivatives of the fold angle are considerably simplified by invoking the small strain/curvature behaviour of the facet. To manoeuver the origami from its initial to final configuration, rest angles defining the zero energy states of the creases are changed to their target values incrementally. The proposed methods of quantifying the bending deformation in Q4 and the derivative of the fold angle are implemented in a commercial software using two user-defined element subroutines. They together with the built-in 3D membrane elements realize the simulation and analysis of origami in a finite element environment. Furthermore, the element for modelling the crease is equally applicable to modelling spring-loaded hinges.

大多数牛至由三角形和四边形的小面组成。由于折痕实际上是笔直的，因此可以将小平面建模为仅具有平移节点自由度的3节点三角形（T3）和4节点四边形（Q4）。尽管在T3中不可能进行弯曲，但在大位移/旋转但应变/曲率较小的情况下，采用了定量考虑来量化Q4中的弯曲变形。相关的切向刚度矩阵证明是一个简单的常数矩阵。同时，折痕的折叠角由连接折痕和定义相邻小平面的节点的两个向量的点积计算得出。通过调用小面的较小应变/曲率行为，可以大大简化折叠角的导数。为了从原始配置到最终配置来操纵折纸，定义折痕为零的能量状态的静止角逐渐更改为其目标值。在商业软件中，使用两个用户定义的元素子例程实现了量化Q4弯曲变形和折角导数的建议方法。它们与内置的3D膜元件一起在有限元环境中实现折纸的仿真和分析。此外，用于对折痕进行建模的元素同样适用于对弹簧加载的铰链进行建模。它们与内置的3D膜元件一起在有限元环境中实现折纸的仿真和分析。此外，用于对折痕进行建模的元素同样适用于对弹簧加载的铰链进行建模。它们与内置的3D膜元件一起在有限元环境中实现折纸的仿真和分析。此外，用于对折痕进行建模的元素同样适用于对弹簧加载的铰链进行建模。