A four-node quadrilateral element possesses two edges that are collinear, as shown in the sketch below. Compute the Jacobian matrix [] =V at a generic position (r,s) within the ly, y %3D 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: N-+rX1-s) (4+Dt- (1+r) N, N, (s+D(a+D| Hint: take a look at a 4 node element with non collinear edges and correctly identify the node sequence first
A four-node quadrilateral element possesses two edges that are collinear, as shown in the sketch below. Compute the Jacobian matrix [] =V at a generic position (r,s) within the ly, y %3D 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: N-+rX1-s) (4+Dt- (1+r) N, N, (s+D(a+D| Hint: take a look at a 4 node element with non collinear edges and correctly identify the node sequence first
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d2a18dd-ae37-4f31-b916-9a3cd7c5056b%2F593312a8-7a0d-4771-b295-19ac2107e61a%2Fxfp0xzs_processed.jpeg&w=3840&q=75)
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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