Finite Element Method in Structural Mechanics - Assembly of System Matrices

Assembly of System Matrices

Adding (16), (17b) and equating the sum to (15) gives:

Since the virtual displacements are arbitrary, the preceding equality reduces to:

Comparison with (2) shows that:

• The system stiffness matrix is obtained by summing the elements' stiffness matrices:

• The vector of equivalent nodal forces is obtained by summing the elements' load vectors:

In practice, the element matrices are neither expanded nor rearranged. Instead, the system stiffness matrix is assembled by adding individual coefficients to where the subscripts ij, kl mean that the element's nodal displacements match respectively with the system's nodal displacements . Similarly, is assembled by adding individual coefficients to where matches . This direct addition of into gives the procedure the name Direct Stiffness Method.