3. assigning forces

Independent Edges

The forces can only be freely assigned to certain number of edges in a given form diagram. The number of edges that can be freely loaded corresponds to the number of independent states of self-stress k defined in Van Mele et al. (2014). In a graph the states of self stress are associated with the geometry by the following equation:

$$k - t =m-2n_i$$

where $t$ is the number of inextensibles mechanisms, $m$ is the number of edges in the form graph and $n_i$ is the number of internal vertices of the form diagram. For all the examples in this tutorial no inextensibles mechanisms exist $t=0$ , such that the number of independent edges can be computed simply by:

$$k =m-2n_i$$

In the examples below we compute the number of independent edges (or DOF) in the form diagrams. The edges highlighted in purple represent a possible selection of the independent/loaded edges. Note that any combination of edges (including internal edges) can be selected as independent in these problems, however, it is more convenient to select the applied loads as independent edges. Based on the number of independent edges in a pattern we can divide the structures usually studied with IGS in three types:

IGS checks the required number of independent edges via the button Check DOF.

We will be interested specially in structures of type A (non-funicular) and C (funicular) which can be asociated with the figure below:

with the definition of the independent edges the equilibrium can be solved in the next step.