## 3. A simple element analysis (cont'd)

The **natural-coördinate** method (Desai & Abel, 1972,
pp. 88-91) expresses the location of any point in the triangular
element by the area coördinates
\((\zeta_1, \zeta_2, \zeta_3)\),
where
\(\zeta_i = A_i / A\); \(A\) is the total area of the
triangle and the \(A_i\) are as shown in the
Figure. (Note that the three \(\zeta_i\) are not
independent, since they add up to 1.) We can use the \(\zeta_i\)
as the set of basis functions. It can be shown
that in this case the coefficients \(c_i\) become the
nodal displacements \(w_i\).
Following the
Rayleigh-Ritz procedure again leads to equation 10.

R. Funnell
Last modified: 2018-11-07 12:52:06
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