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

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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 point P.

written 7.2 years ago by

shahanwazhavale • 90

modified 3.2 years ago by

pedsangini276 • 4.8k

Subject: Finite Element Analysis

Topic: Two Dimensional Finite Element Formulations

Difficulty: Medium

finite element analysis

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1 Answer

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written 7.0 years ago by

teamques10 ★ 69k

• modified 6.9 years ago

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Given,
$x_1,y_1=2,3$
$x_2,y_2=7,4$
$x_3,y_3=4,6$

$x=4.5 \hspace{0.3cm} N_1=0.3$

Now,
$x=\sum N_jx_j=N_1=N_1x_1+N_2x_2+N_3x_3$

$4.5=0.3*2+7N_2+4N_3$

$4.5= 0.6 + 7N_2+ 4N_3$

$7N_2+4N_3=3.9 \hspace{3cm} -eq (1)$

$Now, N_1+N_2+N_3=1 \hspace{1.7cm} -property\, of\, shape \,function$

$N_2+N_3=0.7 \hspace{3.3cm} -eq(2)$

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

$N_2=0.36\,\,\,N_3=0.33$

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