2, 3, 4, columns 1, 2, 3, 4 of [k(b)]. Repeat for remaining elements a and c, to give finally:

«41 «42 «43 + ¿>21 «44 + ¿ 22 ¿>23 ¿24

The above assembly procedure is generally applicable to any element, albeit with detail changes. In the case of the simple beam element, with its rotational, as well as translational dof., reference to § 9.8 shows that the element stiffness matrix is of order 6x6, and hence there will be two additional rows in the dof. correspondence table. A similar argument holds for the triangular membrane element, with its three nodes each having 2 dof. The Examples at the end of this chapter illustrate the assembly for rod, beam and membrane elements.

9.11. Application of boundary conditions and partitioning

With reference to §9.4.7, before the governing eqn. (9.28) can be solved to yield the unknown displacements, appropriate restraints need to be imposed. At some nodes the displacements will be prescribed, for example, at a fixed node the nodal displacements will be zero. Hence, some of the nodal displacements will be unknown, {pa}, and some will be prescribed, {pp}. Following any necessary rearrangement to collect together equations relating to unknown, and those relating to prescribed, displacements, eqn. (9.28) can be partitioned into


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