1. The shape function for the two dimensional rectangular element in Figure 1 are: N₁ N3 1 4ab 1 4 4ab a -(x-a)(y-b) -(x + a)(y+b) L._ Figure 1 N₂ N₁ a = 1 4ab 1 3 2 4ab b X -(x + a)(y-b) b -(x − a)(y+b) Determine [J], [J], and the [B] matrix for the rectangular element for plane elasticity

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. The shape function for the two dimensional rectangular element in Figure 1 are:
N₁
N3
=
=
1
4ab
1
4ab
4
a
Figure 1
-(x− a)(y-b)
y
(x + a)(y+b)
N₂
N4
a
=
==
4ab
1
3
4ab
b
X
b
(x+ a)(y−b)
-(x − a)(y+b)
Determine [J], [J], and the [B] matrix for the rectangular element for plane elasticity.
Transcribed Image Text:1. The shape function for the two dimensional rectangular element in Figure 1 are: N₁ N3 = = 1 4ab 1 4ab 4 a Figure 1 -(x− a)(y-b) y (x + a)(y+b) N₂ N4 a = == 4ab 1 3 4ab b X b (x+ a)(y−b) -(x − a)(y+b) Determine [J], [J], and the [B] matrix for the rectangular element for plane elasticity.
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