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The nodal co-ordinate of the triangular element are shown in fig,At the interior point P, the co-ordinate is (4, 5) and $N_{1}$=0.3.Determine $N_{2}, N_{3}$ and y coordinate of pint P
written 5.9 years ago by gravatar for teamques10 teamques10 ★ 68k •   modified 4.5 years ago
finite element analysis
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written 5.9 years ago by gravatar for teamques10 teamques10 ★ 68k

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Given, $x_{1}, y_{1}$ = 2, 3

$x_{2}, y_{2}$ = 7, 4

$x_{3}, y_{3}$ = 4, 6

x = 4.5 $N_{1}$ = 0.3

Now,

x = $∑N_{j}x_{j} = N_{1} = N_{1}x_{1} + N_{2}x_{2} + N_{3}x_{3}$

4.5 = $0.3 ∗ 2 + 7N_{2} + 4N_{3}$

4.5 = 0.6 + 7N2 + 4N3

7$N_{2} + 4N_{3} = 3.9$ − eq(1)

Now, $N_{1} + N_{2} + N_{3}$ = 1 − property of shape function

$N_{2} + N_{3}$ = 0.7 − eq(2)

By solving equation(1) and (2) we get,

$N_{2} = 0.36 N_{3}$ = 0.33
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