can someone explain what has happend here after the which can be written as please

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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can someone explain what has happend here after the which can be written as please

(b) The first step is to determine the logarithmic strain
[ε(0)] = = = In([C]),
where
2
this gives
4 ln(R/r)
1
[ε (0)]
0
2
0
Which can be written as
200
0 -1 0
[ε(0)] = (In(R) - In(r))
Lo
оо -1
or in vector format as
{e(0)} = (In(R) - In(r)) {2 -1 -1 0 0 0}¹
=
0
2 ln(r/R)
0
[C] = [F] [F]
0
0
2 ln(r/R)
Transcribed Image Text:(b) The first step is to determine the logarithmic strain [ε(0)] = = = In([C]), where 2 this gives 4 ln(R/r) 1 [ε (0)] 0 2 0 Which can be written as 200 0 -1 0 [ε(0)] = (In(R) - In(r)) Lo оо -1 or in vector format as {e(0)} = (In(R) - In(r)) {2 -1 -1 0 0 0}¹ = 0 2 ln(r/R) 0 [C] = [F] [F] 0 0 2 ln(r/R)
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