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 8.0 years ago by

mahendraporeddy123 • 0

modified 4.0 years ago by

krithikkm200 • 10

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 7.8 years ago by

teamques10 ★ 70k

• modified 7.7 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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