Question 12.9.1: Prepare a flow chart to replace Step 3 to Step 9 of that in ...

In Subsection 12.9(c), a flow chart is given for building up the structure stiffness matrix K_s from the stiffness matrices K of the various triangular elements.
This flow chart has the advantage that it shows clearly how the computer can be instructed to carry out the operations involved in the building up of K_s . It has the disadvantage that, if the number of degrees of freedom of the individual elements is large, then a large number of statements or computer instructions is required.

 Table 13.1-2 in Chapter 13 gives a practical flow chart for skeletal structures.

Table 13.1-2. A flow chart for subroutine POST
N = Number of degrees of freedom per joint for the structure under consideration (1,2,3, or 6).
Ks = Stiffness matrix. All terms set to zero before the first member is handled.
El = Joint number at end 1 of the member.
E2 = Joint number at end 2 of the member (E2 > El).
I and J = Two integer counters.

Using the same general approach, a flow chart can be drawn up for triangular elements, as shown below:

Consider the element No. 1 in Fig. 12.9-1; that is, l = 1. The reader should verify that Steps 4 to 9 in the first cycle (with N1=1 \ , \ N2 =1) we post

K(1,1) of element No. 1 to K_S(9, 9)

K(3, 1)of element No. 1 to K_S(1, 9)

K(5, 1) of element No. 1 to K_S(3, 9)

in that order.

He should finally satisfy himself that Steps 2 to 11,† cycled as indicated for

(1) N1 = 1, N2 = 1,
(2) N1 = 1, N2 = 0,
(3) N1= 0, N2 = 1, and
(4) N1 = 0, N2 = 0,

would do the work of Steps 3 to 9 of the flow chart in Subsection 12.9(c).