Continuum Mechanics Homework Review

Problern fr

Prove +he Fol/ou:i,tg resulfs f"r se_cono[ order {-erso.s.

a) t7. (T S) = fn (S T)

b) det(I) = o(ef det5
f
c) ( .s + ' T-\. -/r
v a \
= T-l S-/

d) (eb)(sol) = (n.e)(es()

P rob lem B

'The- c o r n p o ne r r f s of *ensor T wilh r"espcf to o basts
t 9.] o.e

f r s -sl
Irr]l= | s o ol
L-s o tl
Consr'oten q. ina',sFa r"nqlion oS cooroli nq.*es u: herg
F^ope"

,= # (-s.*r9.,) r o'
=
,


q) Fr'no( *he componen{. f*r"r

b) Ver,fy fhe- 3 {urJa'nen*",1 in vq.r tqnfs n{- t




Problem C-

Le.|- A
T e TLye) be sgn'tme-tric-. Thr's t'tt'1 lie-s
p Q4

e - r 'n q e n v e c * O r I r c , si s t ei i e.)c
rrfr u ith cornFo nenls

r( t->, o o II
-
I Y | -
L I Km J lo)'o
Loo,X3 j
l,lse *he- d.el;nilto... of rrniqc',tl in ferrns of lhe
"lete
V."tr-" 0.,'grf
"f,

4e,t (I->4)= (>,*,>) ().-- >) (>, -I)
qn"l

fr=>rt).*>;

X- : >r >i +->r \ t >.\

-4r- = >r >a- >j