2.59. Derive the following relations involving the elastic constants:2K = λ +23³ GG =E =V =X(1 — 2v)2v2G(1 + v)3(1 – 2v)G(3λ + 2G)A + GX2(X+G)3K(1 – 2v)2(1 + v)=E2GE3(1 – 2v)-1=3KE9K- - E2G(1 + v) = 3K(1 – 2v)3K-2G2(3K+G)=9KG3K+ G3K- E6K

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2.59. Derive the following relations involving the elastic constants: 2 K=A+=G G = 3 X(1 — 2v) 20 G= E= V = 2G(1 + v) E 3(1-2v) 3(1-2v) G(3λ +2G) λ + G X 2(X + G) 3K(1-2v) 2(1 + v) = E 2G 1: = = = = 2G(1 + v) = 3K(1 – 2v) 3KE 9K - E 3K-2G 2(3K+ G) = 9KG 3K+ G 3K- E 6K

2.59. Derive the following relations involving the elastic constants: 2 K=A+=G G = 3 X(1 — 2v) 20 G= E= V = 2G(1 + v) E 3(1-2v) 3(1-2v) G(3λ +2G) λ + G X 2(X + G) 3K(1-2v) 2(1 + v) = E 2G 1: = = = = 2G(1 + v) = 3K(1 – 2v) 3KE 9K - E 3K-2G 2(3K+ G) = 9KG 3K+ G 3K- E 6K

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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Question

2.59. Derive the following relations involving the elastic constants:
2
K = λ +23³ G
G =
E =
V =
X(1 — 2v)
2v
2G(1 + v)
3(1 – 2v)
G(3λ + 2G)
A + G
X
2(X+G)
3K(1 – 2v)
2(1 + v)
=
E
2G
E
3(1 – 2v)
-1=
3KE
9K- - E
2G(1 + v) = 3K(1 – 2v)
3K-2G
2(3K+G)
=
9KG
3K+ G
3K- E
6K

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