> For the complete documentation index, see [llms.txt](https://manual-1-3.karamba3d.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://manual-1-3.karamba3d.com/chinese_1_3_3/3-in-depth-component-reference/3.3-cross-section/3.3.3-spring-cross-sections.md).

# 3.3.3: 弹性元件断面 (Spring Cross Sections)

弹性元件允许用户通过其常数直接定义两个节点之间的刚度关系。每个节点具有六个自由度（DOFs）：三个平移和三个旋转。使用**“Cross Sections（断面）”**多元运算器并将**“Cross Section（断面）”**设置为**“Spring（弹性元件）”**，可以通过六个弹性元件常数与这些自由度相对应。两个节点之间的相对运动$$u\_{i,rel}$$将产生弹力$$F\_i = c\_i \cdot u\_{i,rel}$$。在上述等式中，$$u\_{i,rel}$$表示在x、y、z、$$c\_i$$三个可能方向中任何一个方向上的相对平移或旋转，ci代表弹性元件的刚度。在Karamba3D中，平移时，后者为$$kN/m$$（千牛顿每米），而旋转时后者则为$$kNm/rad$$（千牛顿米每度）。输入端口**“Ct”**和**“Cr”**可以分别输入具有平移和旋转刚度常数的向量。它们的方向与它们所使用的局部梁坐标系相对应。在弹性元件是零长度的情况下，默认为全局坐标系，不过可以使用**“OrientateBeam（定位梁）”**对运算器进行更改。

在实现两个节点之间的刚性连接时，弹性刚度的选择会成为一个问题。数值太高会使得全局刚度矩阵条件欠佳，可能会导致数值上的奇点刚度矩阵。数值太低则会导致不必要的相对位移。因此，用户须通过反复测试找出哪个值可以给出可接受的结果。

![图3.3.3.1：弹性元件固定在一端，而另一端则用点荷载加载](/files/-M9XuVZ6gCW6F2mUFz9K)

图3.3.3.1显示了使用弹性元件时必须考虑的特性：即不知道端点的相对位置。这就是为什么弹性元件右端的荷载不会在其左侧固定端产生力矩的原因。


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