The 3D Hooke's law is oy 0₂ O xz O yz 1-v D V V 1-v E U (1+0)(1-2v) 0 0 0 0 0 0 2 22 1-v 0 0 0 0 0 1-2v 0 &xz 0 1-20 Eyz 000 0 1-20 0 0 0 0 0 Ex ww ww Ey Ez Ex where E is the Young's modulus, v is the Poisson's ratio. a) Derive the stiffness matrix and compliance matrix for plane strain condition (ɛ, =&₂ = 0). b) Derive the stiffness matrix and compliance matrix for plane stress condition ( = O₂ = 0). c) Show that for uniaxial stress condition (0, 0, all other stress components are ze Young's modulus can be expressed as E = Ox, and the Poisson's ratio as v = -x E Ex
The 3D Hooke's law is oy 0₂ O xz O yz 1-v D V V 1-v E U (1+0)(1-2v) 0 0 0 0 0 0 2 22 1-v 0 0 0 0 0 1-2v 0 &xz 0 1-20 Eyz 000 0 1-20 0 0 0 0 0 Ex ww ww Ey Ez Ex where E is the Young's modulus, v is the Poisson's ratio. a) Derive the stiffness matrix and compliance matrix for plane strain condition (ɛ, =&₂ = 0). b) Derive the stiffness matrix and compliance matrix for plane stress condition ( = O₂ = 0). c) Show that for uniaxial stress condition (0, 0, all other stress components are ze Young's modulus can be expressed as E = Ox, and the Poisson's ratio as v = -x E Ex
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:The 3D Hooke's law is
0₂
o
6₂
Oxy
XZ
0₂
yz
E
(1+v)(1−2v)
1-v
2
U
0
0
0
U
1-v
2
0
0
0
0
0
1-v 0
0
0
0
2
1-2v
0
0
0
0
0
0
1-2v
0
0
0
0
0
w w
Ez
Exz
0 1-2v|yz)
where E is the Young's modulus, vis the Poisson's ratio.
a) Derive the stiffness matrix and compliance matrix for plane strain condition (&xz = &yz
= Ezz = 0).
b) Derive the stiffness matrix and compliance matrix for plane stress condition (0xz = 0 yz
=O₂z = 0).
E
y.
c) Show that for uniaxial stress condition (σ #0, all other stress components are zero), the
Young's modulus can be expressed as E = ºx, and the Poisson's ratio as v=-²
Ex
Ex
Expert Solution
Step 1: Given
is the Young's modulus, 
is poisson's ratio.
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