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Transformer Engineering, 2nd Edition by S.A. Khaparde, S.V. Kulkarni

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Ve=j=12NjeVje.

(12.94)

Image

Figure 12.10 1-D Shape functions.

Nje denotes the interpolation or shape functions which are given by

N1e=r2erleandN2e=rr1ele

(12.95)

where le=r2er1e. The functions Nje, which depend on the independent variable r, are shown in Figure 12.10. N1e(N2e) equals 1 at node 1 (2) and zero at node 2 (1); at any intermediate point its value is a fraction between 0 and 1. This is an obvious result given the expression, as in Equation 12.94, for voltage at any point within the element, Ve=N1e1e+N2e2e. For example, at node 1, Ve=V1e leading to N1e=1 and N2e=0. Thus, for the nodes, (Nie)j=δij, where δij = 1 ...

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