compas_ags.ags.form_identify_dof

compas_ags.ags.form_identify_dof(form)[source]

Identify the DOF of a form diagram.

Parameters

form (FormDiagram) – The form diagram.

Returns

• k (int) – Dimension of the null space (nullity) of the equilibrium matrix. Number of independent states of self-stress.

• m (int) – Size of the left null space of the equilibrium matrix. Number of (infenitesimal) mechanisms.

• ind (list) – Indices of the independent edges.

Notes

The equilibrium matrix of the form diagram is

$$\begin{split}\mathbf{E} = \begin{bmatrix} \mathbf{C}_{i}^{t}\mathbf{U} \\ \mathbf{C}_{i}^{t}\mathbf{V} \end{bmatrix}\end{split}$$

If k == 0 and m == 0, the system described by the equilibrium matrix is statically determined. If k > 0 and m == 0, the system is statically indetermined with k idependent states of stress. If k == 0 and m > 0, the system is unstable, with m independent mechanisms.

The dimension of a vector space (such as the null space) is the number of vectors of a basis of that vector space. A set of vectors forms a basis of a vector space if they are linearly independent vectors and every vector of the space is a linear combination of this set.

Examples

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