The following example shows how to define compatibility conditions in nodes for the corresponding displacements. The following drawing shows an example of a structure.
The following nodes and bars have been defined in this structure (see the drawing).
Nodes:
No. 1 with the following coordinates (0, 0, 0).
No. 2 with the following coordinates (2, 0, 2).
No. 3 with the following coordinates (1, 0, 1). Nodes No. 3 and 6 have identical coordinates.
No. 4 with the following coordinates (0, 0, 2).
No. 5 with the following coordinates (2, 0, 0).
No. 6 with the following coordinates (1, 0, 1). Nodes No. 3 and 6 have identical coordinates.
Bars:
No. 1 Starting in node 1 and ending in node 3
No. 2 Starting in node 3 and ending in node 2. Bars 1 and 2 add up to form the first bar "I"
No. 3 Starting in node 4, and ending in node 6
No. 4 Starting in node 6, and ending in node 5. Bars 3 and 4 add up to form the second bar "II".
Compatibility type is defined in such a way that node displacements are identical, while rotation in nodes can differ.
The compatibility of nodes 3 and 6 with respect to displacements UX, UY, and UZ means that bars "I" and "II" have identical displacements in the common node 3(6), while their rotations differ. Such a definition is equivalent to a hinge consisting of two continuous bars "I" and "II".