Finite elements from different structural elements are connected by their nodes only if there is a connection between the associated geometric entities: points, curves, surfaces, etc.
If node connectivity does not exist, it may cause singularities such as unconstrained degrees of freedom. Therefore, the stiffness matrix becomes non-positive and analysis ends with a solver exit message. The left figure shows a congruent mesh while right figure shows a non-congruent mesh.
To ensure a congruent mesh, adjacent high-order geometric entities must share coincident lower-order entities. Here, there are some examples:
Beam Structural Elements: Adjacent structural beam elements will share boundary nodes if their associated lines share a common middle point. To obtain the following 3 span beam with congruent mesh.
Each line must be defined by means of Referenced Points previously created: In this way, lines will share common points (P2, P3) and only one node generated at these locations.
But, if the same model is performed by three continuous lines which are defined with points on the fly (Non Referenced), then two points are created (internally) for each line. This results in a total of six points, two points existing at same location (P2-P3, P4-P5).
Two pair of nodes will be generated at common sharing points and singularities may appear in solving process due to unconstrained degrees of freedom as different beam structural elements are not properly connected:
To force continuity in mesh, geometric entities must be shared (points, curves, areas or volumes). If geometry is not connected then mesh is not connected (duplicated nodes exist).
But if geometry is connected then mesh is connected (duplicated nodes do not exist).
