Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

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3
3
where n is the boundary normal. The above equation can be rewritten for the node I
in Fig. C.1(b) as
ÿ B1
6 …2FI i ‡ F 3 i †n 1 ‡ ÿ B2
6 …2FI i ‡ F 1 i †n 2
…C:6†
where ÿB1 and ÿB2 are appropriate edge lengths.
The above equations (C.3) and (C.5) can be reformulated for an edge-based data
structure. In such a procedure, Eq. (C.3) can be rewritten as (for an interior node I)
X
…
E 2 I
I
E
1
2
@N I
…N
@xi k F k i † d ˆ Xm s
S ˆ 1
2
(a) (b)
Fig. C.1 Typical patch of linear triangular elements: (a) inside node; (b) boundary node.
X
E 2 II s
A E
3
@N I
@x i E
…F I i ‡ F Is i † …C:7†
where m s is the number of edges in the mesh which are directly connected to the node
I and the summation P E 2 II s extends over those elements that contain the edges II s.
The user can readily verify that the above equation is identically equal to the standard
element formulation of Eq. (C.4) if we consider the node I in Fig. C.1(a). The
inclusion of boundary sides is direct from Eqs (C.5) and (C.6).
3
1
I
2
2
Appendix C 299
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