ABSTRACT
Finally, substituting Eq. (12.195) into integral D, integrating, and evaluating the result yields
(12.204)
where F denotes the average value of F(x) over element (i). Substituting the results for A, B, C, and D into Eq. (12.194) yields the first element equation for element (i). Thus,
(12.205)
(i)Next, let W(x) = N i+1(x). Then,
and (12.206)
Substituting Eq. (12.206) into Eq. (12.193) and evaluating integrals A, B, C, and D yields the second element equation for element (i). Thus,
(12.207)
Equations (12.205) and (12.207) are the element equations for element (i). Next let's assemble the element equations to obtain the nodal equation for node i.
Figure 12. 19a illustrates the portion of the discretized global physical domain surrounding node i. Note that fu:i_1 = Xi - Xi_I # fu:i = xHI - Xi. Consider element (i - I) in Figure 12.19a. Node i in element (i - I) corresponds to node (i + I) in the general element illustrated in Figure 12.19b. Thus, the element equation corresponding to node i in element (i - I) is Eq. (12.207) with i replaced by i-I. Thus
