Tva

1(T

" 7.434 x 1(T6 -5.833 x 1(T6 -1.505 x 10"3 0 0 0

176.60 x ltf

22.20 x ltf

N/m2

The required element stresses are therefore a\ — 176.60 MN/m2 (T), a" = 96.52 MN/m2 (C), o'3 = 100.42 MN/m2(C) and erf = 22.20 MN/m2 (T).

Example 9.5

Derive the stiffness matrix in global coordinates for a three-node triangular membrane element for plane stress analysis. Assume that the elastic modulus, E, and thickness, t, are constant throughout, and that the displacement functions are u(x, y) — ot\ + a2x + a3y v(x, y) = a4 + a5x + a6y

Solution

With reference to §9.9 and with respect to the node labelling shown in Fig. 9.41, matrix [A] will be given as:

Apa I APa_

0 0

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