The reference and deformed configurations of an object experiencing two-dimensional motion (U3 = 0) is shown in the figure below: X₂ D(0,1) A(0,0) C(1,1) B(1,0) Reference Configuration Note: Type the original position in capital letters (i.e. X1 and X2) X₁ The deformation gradient is: X₂ The displacement gradient is: A' If the coordinates of the deformed square are A′ = (10, 10), B′ = (17,11), C′ = (18, 18), and D′ = (11, 17), determine the following: F (a) The two-dimensional position functions that describe the motion shown above. The position functions are: #₁ I₂ (c) The deformation gradient F and displacement gradient Vu. Vu= D' (b) The two-dimensional displacement functions that describe the motion shown above. The displacement functions are: ₁ 242 B' Deformed Configuration X₁
The reference and deformed configurations of an object experiencing two-dimensional motion (U3 = 0) is shown in the figure below: X₂ D(0,1) A(0,0) C(1,1) B(1,0) Reference Configuration Note: Type the original position in capital letters (i.e. X1 and X2) X₁ The deformation gradient is: X₂ The displacement gradient is: A' If the coordinates of the deformed square are A′ = (10, 10), B′ = (17,11), C′ = (18, 18), and D′ = (11, 17), determine the following: F (a) The two-dimensional position functions that describe the motion shown above. The position functions are: #₁ I₂ (c) The deformation gradient F and displacement gradient Vu. Vu= D' (b) The two-dimensional displacement functions that describe the motion shown above. The displacement functions are: ₁ 242 B' Deformed Configuration X₁
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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Transcribed Image Text:The reference and deformed configurations of an object experiencing two-dimensional motion (13
▲ X₂
D(0,1)
A(0,0)
C(1,1)
B (1,0)
Reference Configuration
Note:
Type the original position in capital letters (i.e. X1 and X2)
X₁
The deformation gradient is:
X₂
The displacement gradient is:
A'
F
If the coordinates of the deformed square are A' = (10, 10), B' = (17,11), C′′ = (18, 18), and D' = (11, 17), determine the following:
(a) The two-dimensional position functions that describe the motion shown above.
The position functions are: #₁
I₂
(c) The deformation gradient F and displacement gradient Vu.
Vu
D'
(b) The two-dimensional displacement functions that describe the motion shown above.
The displacement functions are: ₁
22
B'
Deformed Configuration
X₁
0) is shown in the figure below:
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