2. Consider a fourth-order polynomial approximation 0e (x) = a, + a2x + a3x2 + a4x3 + a5x* applied to an element e covering the domain of x E [0,8]. Assume all nodes are equally spaced: a. Construct the element shape functions. b. Find the approximation for displacement field if de = [0, 2, –1,1,3]. c. Calculate the Be matrix and approximate the strain field using Be and de in b.
2. Consider a fourth-order polynomial approximation 0e (x) = a, + a2x + a3x2 + a4x3 + a5x* applied to an element e covering the domain of x E [0,8]. Assume all nodes are equally spaced: a. Construct the element shape functions. b. Find the approximation for displacement field if de = [0, 2, –1,1,3]. c. Calculate the Be matrix and approximate the strain field using Be and de in b.
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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![2. Consider a fourth-order polynomial approximation 0e (x) = a, + a2x + a3x2 + a4x3 + a5x*
applied to an element e covering the domain of x E [0,8]. Assume all nodes are equally spaced:
a. Construct the element shape functions.
b. Find the approximation for displacement field if de =
[0, 2, –1,1,3].
c. Calculate the Be matrix and approximate the strain field using Be and de in b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc1f0895-3e88-478e-9b57-bd5425e70952%2F52aa3e19-645c-4fe1-9662-4e0e10df0c5f%2Fmugdloi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider a fourth-order polynomial approximation 0e (x) = a, + a2x + a3x2 + a4x3 + a5x*
applied to an element e covering the domain of x E [0,8]. Assume all nodes are equally spaced:
a. Construct the element shape functions.
b. Find the approximation for displacement field if de =
[0, 2, –1,1,3].
c. Calculate the Be matrix and approximate the strain field using Be and de in b.
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