Chapter 1 Fundamentals in Elasticity
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- Joanna Flowers
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1 Fs s ν
2 . Ioo ssfo of ss Ms 분체역학 G Ms 역학 Ms 열역학 o Ms 유체역학 F Ms o Ms 고체역학 o Ms 구조해석 ss Dfo of Ms o o w oo of os o of fos s s w o s s. Of fs o o of oo fos os o o o. s s o s of s os s o s o o of fos o. G fos o s w os o o of fos; s s s of s o. W s ss Ms? oo of os foows Nwo s ws of oo. - w of - w of o : F - w of o o Wo s? - G Go 6 ~ 6 H o oos of os s o oso o o. Hs
3 foo of w of f os o os of f s of oo. H ss s of so w of s w oso fo q o o o H z o s oz o fo so fs of. Ufo o oos ow s s s w ffo o s f o s oos of os o w. - Iss Nwo 6~ 77 H o foos of ss s Go of ffo o w so oos G Gof W Lz 66~76 os s.. - Wo s? W s of sss s s R. Hoo 6~7: Hoo s Lw Jo. o 6~7: o s o D o 7~78: o s fo s fow L. 77~78: qo o. Yo 77~89: Yo s os f of. 789~87: s s fos of o Fs os - Dff M Pos F fows s G <<. o os o s G. Is f: G sos f: << G << - F s f so s os. - f so s fo fo s fwo. - oo M Ioo o s of oos s
4 w so f o s sos. s Ps L Pos - os w s M: Ros o ss of o w os o. - s os o o. - - os w Ps M: o o o ss of o w os o. P foo s os. - L Pos: of soso s. α α - s os o o. ssfo of Pos D Pos : f ss s I Rsos Is Pos : Roso o I s Ms Rsos Is Pos : s Ifo o I o s o Ms Rsos
5 . Po Dfo ν Ps s - Do o - M os - o oos : o o w Uows o: - ss - - Ds W ows s o qos o so s os. w ows o fo s o oos s os of o os. W w o s s ss: - ss - - Ds - Ross o ows s s q s-s os s-sss os
6 6.. Do o
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8 .. os 8. Nwo s ws of oo s w of os.. o s o o of fo.. ss s f w o.. sss o s o s of of s s o. P f P P P Fo - P f P P w o s. z osq of s o? If sss o w f ss o os sss-s o so s s of s o s s of s w ss ff qos. ow s o ss sss o s o s s o sss o s of s s of s. sss-s o s os of o s ss s o 6 qos o of o qos o qos ff qos w s os s. s sss o s o o of s o sss-s o os ff qos o.
9 9.. sos Oos so oo : I oo : o oo : sss o sss os so. s s. Do o o o of wo s ss so o s of fs s fs of so. oss o of wo os s G oo
10 Ko fo fo Po so wo s q fo o o fo o D of D D I D
11 so fs I s oo oo s f f so f of : z z o f so f of : z z so f of : z z so f of : z q qs z s D Gss o z z F F F F F F F F F F F F F F F
12 o ss
13 .. o ss F F F o: Δ ss : z oos of o
14 .. Dfo of ss z z z z zz z z z z z zz z
15 .. s o Ro q oo os os os O O O O O O ρ ρ s o fo of sss s O O
16 6.. q qo - I o Fo q: F fo ρ o s os fo fo q qo os ρ ρ o qo so ssf fo os q so s w o. ρ ρ ρ Mo q: M fo ρ o fo os ρ
17 7 ρ ρ I s s o o o.. oso Po Pos oso G O o oo o o sf o o fows o o o o. oo s fows o o wo ff o o f o. fo oso of o f s ss s: f
18 s s s -fow o s s os o. s ow o o ws os os of o fow o so oos o ow o o of sf. o w. z f f f qo so o fo sss Po Pos f I o o o f of ss s f of s fo f o s o fo Φ 8 fos L qo fo os ss. f Φ f ss os ooos soo Φ f Φ f Φ f o Φ Φ Φ z f Φ f
19 .6. q Po Pos 9 q Fo q: F F Fz o F o fo os o D o qo so o fo sss q. fo Mo q: M fo o M Po Pos fo o I s s os o os o w os o so. How s o fos. fo o s oo of sss sss oo so fo of s of oos of o fos fo os so f s fo o so so o so: : o
20 I s q qo s of o fos: :.7. Roo of s ss os w oo ss s f w w o sss oo of o oo ss. Roo of s w Ooo Τ Τ Ι Dff Oo z z P
21 os oo ss os os os o os o s o o so sfo o s sss. ss oo ss
22 q qo oo ss - ss: o fo: D: - q qo s of so of oo ss.
23 Ds
24 .. K Dso Ks? sso of ss s o w o oss oo of o o ss of os wo oso of fos o.. ss ffs of oos. Ks Dso Dso of s oso of os o sss of s w s o o w o s o Do w o o of s s? How o s ff oo of O Hw? - Mo I: D o ow o O w s o of o w. If o ff s o w s o o of o o.
25 f If o of o w s s o o o fo o o so of ff oo of O w. No ff s o fo os w s so so s. Mo II: ow oo of o o w os o os of s ss fo of o. If s s oo o w o so o so of ff oo of O w. If o ff o o oo o f Is Nwo o o. s s s o s of os of wo s ss o o sfo oo wo ff. f No oos of wo ff s s ff s s s oo. o os o of so of s ss f s o s o w o ss o so so s os w s so f s. Rf L Dso: Mo I I s oso of os f ofo. I s f ofo s s os o o s oso ow. W f ofo s os o ofo f so s L so. f oso s s fo o fo o oso f
26 ofo. s os s fos of. No os o oso f ofo o s s o. Rf ofo 6 X X X Dso: Mo II s s oso os. s so fs o o o of s oo o s of o o of. s o f oso fo ff. I s so os s f s of so w s s N-os qo os ooos ff qo f. oo o: ss o
27 7.. Ds Ds o s s s s α s s α α α s s G s s.
28 8 s s α α α α s s s s. G s s of s α α α α α α α α α α α α α α α α α α ] [ ] [ ] [ α α α α α α α α α α α α s fs s so foo fo s s << I s s s of s s.
29 9 R o oo : s s s s fo. fo wo o. Fo s s. s : γ fo oo oo ss D : α α α α
30 .. Ps Ms No Fo o s s s s s s s s s s s s s s s s s s fo s s s s s s s ss os os ss s s s s os s α s α I s << s α α
31 .. o -D Pos I s s f s os q s f oss s? - I s s oos s s oos f wo. - W f s s oos o f s of o? w ws s oos q? - s s oos o s oos s. - W o ows s s qos w s oss o so. fo s oos o. - o oss w s oos so f. - W f o o oos s o oo! W oos s q o o so? wo so s : f f γ s f o f!!!
32 .. G s P I oo fo s - s f so s- fos w of. - s oo s o so o fss of s. Ω Ω Ω Ω Ω Ω Ω Ω Ω F Fo oo F F
33 ] [ ] [ ] [ ] [. so.- s o qos U U U R R R W o qos s qos s. W s? fos R U U U R U U U R
34 fos sow. s qos o o qos o of s. Ufo w s o o ss o so of oss o of s! D of o K. Wsz 97 os o s of o qos ssf o w o s ssf o o. o qos sf o o o ssf o. fo o o s of o qos s q o ssf o o o o. - s U U U R R R o. oo z R R R R R R - s z R R R z U U U o. oo U U U U U U. Fo z F z G z H [ ] [ [ F M U F H U G H U U F G U H F U H F U U H U U G U U F I z F z G z H z U U U.
35 os Ros
36 6.. os Lw Gz Hoo s Lw Go qos so s q : ρ -s o : os w : q qos s of s ρ o oos Ds : o Γ o : o Γ o s of s.. Isoo M Isoo? Iso s o s o s o sos o ss. Isoo ss fo o sos o ss. fo soo s os w s o s os. I o wos os of so of s. ss of s so o of off: 8
37 7 o : 6 w.. : 6-6/6 I Ros R. off # of off. # of I. R. N-N N-O.N. - -O. N- -N 9 o No- Ro s I s II s I I s II II soo oo I II fo.
38 -O Ro 8 s I s II s I I s II II soo oo fo. I II 9 Roo ssos R. off o N-N N-O.N. - ssos ss s os.
39 oso 9 Roo of ss q q Fo soo q q q q q q q [ [ [ q q [ q q q ] ] ] q q q q q q q ] q q q q q F Ro: wo off λ µ L s os λ µ D ssos λ µ λ λ µ µ µ λ µ λ µ λ λ λ µ λ µ µ µ λ λ µ µγ µγ µγ λ λ
40 q qo s of L os ρ λ µ ρ λ λ µ µ µ µ ρ λ µ µ ρ.. Ps Ms of M Pos Yo s Mos Posso s Ro & L os ρ L -ν L ν ν ν ν ν ν
41 ν λ µ G Ps Do of Mos τ τ τ τ τ τ τ τ τ τ τ ν ν [ ] os γ s γ s γ γ γ τ ν τ γ τ Gγ ν G ν
42 oo
43 .. q qo Fo Rs Q Q q Q q
44 Mo Rs M ~ ~ ~ w ~ Q M ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Q M oo fo q Q q q Q q q Q q M ~ Q M Q M
45 P Q q M Q M q M W oos so ssf o os o o s oso of??
46 6.. o s sso o s f so s f foo. No s o. s s os o of. Ds oos sso z?? -s o -ss o zz z z?? γ γ γ z z z z ν ν ν z z z z????
47 7 sso o sss o zz?? ν zz ν zz ow s-s o Posso o so zo w s q o Posso ff. M z I M q I q M I so w fo s o 6 q 8 q 8 6
48 8.. oso s sso o s f so s f foo. No s o. s s os o of. Ds oos sso?? z oos zz z z?? γ γ γ z z z z z z z?? z?? q qo M q
49 oso 9 ~ γ G GI Q f G s G γ w G γ M G I G I I G G q
50 6 P Pos s oo s z
51 6.. P ss z sso ss of s s o o o sos of. No z- o o s o sf. o of sss o ss s. o o oo O ± : ± ± ± ± z z z zz sso z z zz q qo -Ds os
52 z : o ff o soo os w ν ν ν ν ν zz G G Ds o ss s of s G q qo s of s o qos o ssf. Fo o o Fo: Po F ψ ψ s ss fo ψ ψ q qo: ssf
53 ψ ψ ψ ψ s s of sss fo G ν γ ψ ν ψ ψ ν ψ o qo γ ψ ν ψ ψ ν ψ ν ψ ν ψ ψ ν
54 6.. P z sso If z-o w so. I o z-o No z- o o s o sf. -Ds Ro z zz z z z z z z z os w zz zz ν zz ν γ ν ν ν ν ν
55 6. Poo ss Fos o oo w/o o fos ss oos o o os sss ss O
56 6 L sss ss - o o : ss : os o sss s sss Fo o :
57 7 Mo. sss Mo N. sss Ff o f f :
58 8 F oo off of oo so s so o o oos ssf. os o sf w s s sf o.f. s o. s f s o s f. - s P I soss f o os o of o s q o so ffs o sss so o os wos s fo s o o s w os of.
59 6.. 9 L o o oos o ± ± ± o sso ss sos o. o oo o ± ± q ss P P P P I P I M I
60 Ds 6 γ P ν I νp ν I G P IG Io P νp f I I f s s P I νp f I P f IG P I P I f νp I f νp I f P IG f P P IG IG P F F IG F F so os. P f νp f P F F I I IG Io of F F P νp P f f 6I 6I 6IG Ds oos P I νp I νp P 6I 6IG P 6I
61 6 Ds o oos o P I P I νp P 6I 6IG νp P 6I 6IG P I νp 6I P 6IG ow oo s oss. νp P ν νg ν 6I 6IG ν -Ds o νp P νp P I 6I I 6I o P W w sss soo s o ssf!!! W??? Qso o D P w o oss o o oo fo IG o oos so os o o sf q o o os. How o s o oos q o o oos of o sf o oos fo s o. If so w o o s o oos?? w s foo s o oos. D o s so. P 6I P 6I
62 6 P P P I I I P P I GI P νp P P P I 6I 6IG I GI νp P P P I 6I I I fo of soo νp I P / I ν.% fo. P νp P P P I 6I 6IG I GI P νp P I 6I 6GI soo ν. P P I I P P /.7% GI I P P ν /.% 6I I fo. ν. P P P I I I P GI P P I GI P νp P I 6I 6IG P P P νp P 6I I I I GI
63 6.. 6 o o oos. o - q q. o. o -. o oos. so o o o os.. so -s w s o so o fo w. o of fos. Fo M oo. Fo M oo Fo M oo
64 6. Fo M oo Fo M oo. Fo M oo F ssos of ss oos o oos o oo q o oo o sos qos I q q I q q q
65 6 s q oos s q oo : ± I q s q oo : ± I q I q I q f sso fo sss I q I q I q I q s q oos: q ± q I q
66 6.6. s oo 66 X s X os f I s s fo o os fo s s s f s αf o qo fo o s fo. α f α f f G soo ss oos f os α s α os α s α s α[ α α os α α s α α α os α α s α] s α α os α s α[ os α s α os α s α] α osα[ α sα α osα sα α osα] α os α sα o o oos o s α o s α Io oss s α α os α α s α α os α αs α α s α α αs α α s α α α os α α s α α
67 Fo offs 67 q s q s Rf o. -6 of o of s oso.
68 68 7 P Pos Po oo s
69 7.. Po oo ss 69 ss os s z z os s s os s os os s sfoo os s s os ss os s s os z z z z zz os s s os
70 7 z z z z z z os s os s s os z z s os s os s s os s Ps Do of q qo. F F o s os os s s
71 7 o Ds s os?? os s?? os s?? ss Fo os os?? s???? s s s os os s s s os s s os s os os q qo s s???? os s s os s os s??
72 7 Ds os s s os z os s z z z z z zz s os os s s os - z z z z z z os s os s s os z z s os s os s s os s s os os s os s s Go o of s oos H F H F D D F
73 7 / ' F F F / / o
74 7.. Go qo o oos q ss Fo o 7 oos os Lw Ds o oos s Ro o o oo
75 7 7.. oos Po oo s o qo I s s fo of o oo of o qo D D ss oos - If o o ss o of oos - sso w s o s- fo.
76 Ds sss 76 ν ν [ ν ν ν ] ν [ ν ν ν ] f ν f ν [ ν ν ν ] f f f f f f f f f f f F f f H s K os so of o soos o o q.. f ν [ ν ν ν ] H s K os H os K s F R o so os s s os K H
77 77 R o oo F
78 P Po o O : O : o o o o ss oos o o o o Ds ] [ ν ν o o o
79 79 oos P s o zz zz ν ν P sss o o zz zz ν ν os w R P o o zz zz zz z F ν ν o zz o zz ν o ss : > Ds : ] [ ν ν
80 8 7.. ss w ss: << ] [ ν ν If Ro w ss: / / ] [ / ] [ ν ν ν ν s ν If Ro w L Ro o o o o ] [ ν ν o o Ro o o ν
81 8 o ] [ o o o ν ν ν ] [ ] [ ν ν ν ν ν o o o ] [ o o o ν ν ν o ν ν o ν ν ν o o
82 M M o oo O : O : Mo M ss oo o o Mo oo M D M
83 oo w N ss. M N M N M N 8 M N M N Ds ν [ ν ν ν ] H s K os H os K s F Ds.. w o. / F H o : α o oo α 8 α 8 Mo q o os M α N 8 αn M 6
84 7.7. Ro Ds 8 ω f fo : ρω q qo ss s ρω ν ν ν ν ν ν ν ν q qo s of s G oo ρω - qo [ ν 8 ρω ]
85 8 8 8 ] 8 [ ] 8 8 [ ρω ρω ρω ν ν ν ν ρω ν ρω ν ν ν ν o s 8 8 ρω ρω ρω ρω ρω 8 ρω Ds w o ρω ρω ρω ρω ρω ρω ρω ρω s /.9 / s / f N oo fo o Ds w wo ff owo
86 7.8. P w o 86 ss o o f s os s s os s os s os s os os s s oo fo fo sss o >> oo fo o-fo sss f o : os s ss Fo : f os
87 87 o qo D D f D H K D H K K K H K f f f D f f f D F F F F F F F f f f F f f f os os ss oo s 6 6 os 6 os 6 D D s D D D D s D
88 88 F oo os os s ss oo o os : : osso : s o o - - o Oos os s s os os os os os ±
89 7.9. F soo -D osssq oo 89 o oo o ± q oo / / os P fo. f f f f f f os s s of sss / os / os P / / ss oos Po P os ss oos s P P os os os P s os s P s os s os
90 9 ooo I If ξ f f-ξ Mo s R f ξ ξ ξ R f ξ ξ ξ R Pf Pf P f f f M M f f
91 9 8 Ufo oso. oso
92 8.. ss 9 z Ds os α ϕ osϕ osαosϕ s αs ϕ osϕ s αs ϕ α α s α ϕ s ϕ s α osϕ osαs ϕ s ϕ s α osϕ α α z : oo W fo α z ψ oos zz z z z z ψ z γ γ γ z z z z z z z z z ψ ψ z z ψ ψ z
93 9 ss oos z z zz ψ G ψ G q qo z-o o z z z zz ψ ψ ψ ψ G o f o o sf fo z z z fs wo s o ssf z z z z s s ψ ψ s s ss fo z z ψ G ψ G ψ o os s s G s os o o. s
94 9 s of z z M z z X X Go qo : G o oo : ws o : M
95 9 8.. oso o so ss fo G G G G G ws G G G M G M M ss M M z z W fo G M G M f G M G M ψ ψ ψ ψ f f M M M M ψ
96 96 ψ M ψ ψ Fo so w os o o
97 8.. R o s oo 97 Go qo s: o ± ± s so OD -o o s o ± Y ± G os Y s o ± ssf. / G G os os 8 Y Y G / 8 / Y Y G fo / Y s os G ± s os G G os / / / Y / os / G os /
98 98 F oo / os / os os / G ss / os / os s 6 / G z / os / s os 6 / G z M ss 8 7 / os 6 / os 6 / os s 6 / z G G G G ws 96 7 / 9 / 6 / os / s 6 / os / os os 6 / G G G G G M Now so / G G M
99 q so.8.79 / M G G G 99 O so w os ss M G w
100 9 Mos
101 9.. Po Dfo ν Go qos o oos q qo : os Lw : D : -Ds Ros : Ds o oo : o o o oo : o s Ro o o : o oso Π Π
102 Fo s o of s s f o. - 6 of o of s oso o Po Π Γ Γ
103 9.. P of M Po D D D D D D D D D D D D D D Π Π Π Γ Γ Π Γ Γ Π Γ Γ Γ Γ Γ Γ Γ Π Γ Γ Γ Γ Γ Γ Γ Γ Γ Γ Γ D s os f D > fo. fo D > fo D ff.??. q s os o fo Π Π
104 9.. P of Wo If foow q s fo α of wo os. υ Π α Π RR RR ss fo RR D D D D D D D υ Γ Γ α α Γ α α α α Γ α α α α α Π α Γ Γ Γ Γ Γ Γ fo ss If of wo os of o os s ss o qo of of o ss. o so of of wo s Γ Γ fo ss
105 9.. R-Rz Dszo oo P of M Po Γ Π Γ D q q M f K D D D D D D q q q q fo Γ Γ Γ Γ Π Γ Γ Γ Γ P of Wo fo fo f K D D D q q q q q q q q Π Γ Γ Γ Π Γ Γ Γ
106 6 M Fo Wo sso γ γ γ Γ Γ Ds N γ γ γ Γ Γ
107 7 ss-s s Ro D D γ γ γ ν F s qo D Γ Γ Γ Γ Γ Γ N N f K N N D Γ Γ o ss fo
108 8 9. soo s f of s s ss s 6 ν ν ν ν 6 6 D N ν ν ν ν ν ν ν ν ν ν ν ν ν ν z z K P P f P
109 9 ν ν ν ν ν P P I P I P ν ν ν 6 P I P I ν ν P I I M I M I P 6 τ ν
Chapter 1 Fundamentals in Elasticity
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