Structure of global stiffness matrix Global stiffness matrix K is completed by additions from element matrices, as described in detail in the illustrative example of FE algorithm. For large and complicated structures, this addition can be made in different ways and is connected with the node numbering of the mesh. We shall present this on the example of a four-element plane triangular mesh according to Fig.7-1.FE algorithm Fig.7-1 Different node numbering of triangular mesh Global matrix of deformation parameters The first element of 7-1a) mesh contains the deformation parameters u 1, v 1, u 2, v 2, u 4, v 4. They occupy the position no. 1,2,3,4,7 and 8 in the global matrix U. This means, that the element stiffness matrix of the first element will be distributed into the rows and columns no.1,2,3,4,7 and 8 of the global matrix K :

Adding the element matrices of all the four elements into the global matrix according to the algorithm described in Chapter 2, we obtain finally the following structure of K matrix: Again, we can see the banded structure of K matrix, quantified here by so called bandwidth, which is the distance of the most distant non zero element among all rows from the diagonal. In this example, the bandwidth is equal to 8.

We can now repeat the whole procedure for the mesh, numbered according to Fig.8- 1b). It is easy to show, that the K matrix now has the most compact form with the bandwidth equal to six: So the mesh numbering has an influence on the K matrix structure and this is important for the time necessary for solution of the basic equation K.U = F : solution time ≈ (number of unknowns). (bandwidth) 2