Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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A four-node quadrilateral element possesses two edges that are collinear, as shown in the
sketch below. Compute the Jacobian matrix [/] = at a generic position (r,s) within the
element. Investigate where, or under what conditions, J| will be zero or negative.
(0,a)
(a/2,a/2)
(-a.0)
(a.0)
Remember the shape functions and their derivatives are:
(-10-s)
(1-s)
N,
0+s)
(4+Dt-
1+r)
0+r)(+s)*
N,
(1-1)
Hint: take a look at a 4 node element with non collinear edges and correctly identify the node
sequence first
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Transcribed Image Text:A four-node quadrilateral element possesses two edges that are collinear, as shown in the sketch below. Compute the Jacobian matrix [/] = at a generic position (r,s) within the element. Investigate where, or under what conditions, J| will be zero or negative. (0,a) (a/2,a/2) (-a.0) (a.0) Remember the shape functions and their derivatives are: (-10-s) (1-s) N, 0+s) (4+Dt- 1+r) 0+r)(+s)* N, (1-1) Hint: take a look at a 4 node element with non collinear edges and correctly identify the node sequence first
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