CG38.PDF
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- こうじ たかひ
- 5 years ago
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1
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3 PC
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11 - -
12 -3
13 φ θ r (,, -4-5
14 φ θ r (,, -6-7
15 ( ( t s r e w w w M M M M M Z Y X M Z Y X,...(,,,,, Z Y X M M Z Y X M Z Y X M M t s r e, : :, :, : : z y x e S S S M d b f e c M s...( z y x t T T T M 3...(... z y x r M Z Y X z y x : : :
16 cos si si cos x x x x x θ θ θ θ cos si si cos y y y y y θ θ θ θ 4...( cos si si cos z z z z x θ θ θ θ r M t M 5...(... i t r v M M M M 8 : : Z M M i v
17 P ( X, Y, Z P ( X, Y, Z -8 P X, Y, P X, Y, ( Z ( Z P P hx / Z, hy / Z, hx / Z, hy / Z, h...( 6 ( h ( X X Y Y Z > Z P P ( X ( X * v, Y, Y v *, Z, Z v *,(/ W, M p M * j M u ( X ( X *, Y * d, Y, Z * d, X, W * d,...( 7 M u M p / h M j...( 8 M M M u p j : : : 8
18 -9
19 - -
20 -
21 -3
22
23 3-3-
24 i X i X i Y Y Y Y i Yi Y Y Y i X i X i X i X i Y Y Y Y i Yi i Yi Y i X X X X i X i
25 3-5
26 t (/ t (/ Y t (/ X 3-6
27 Y s z z s X 3-7 (, (, α / > ' ' c (, ( c, c ' ' ' ' (, (, (, (, c ' ' (, s z
28 , ( / h h < / < α s, / (,, / z s z s h h h h,, ( / / < < α ( (, z s (, ( z s,,, ( / / < α ( ( ( (, ( ( } {(, ( } {( ( z s z s,, X X X X
29
30 3-3-
31 3-3-3
32 ( x >, y < x ( x >, y >, y x, y x ( y >, y > x ( x <, y >, y x, y x ( x <, y < x ( x <, y <, y x, y x ( y <, y > x ( x >, y <, y x, y x ( x, y θ l { l (/}cosθ l ε {l (/} cosθ ε l l ( ε /cosθ (/ l ( ε /cosθ (/ ε l
33 Y / l θ { l (/}cosθ (/ cosθ X
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39 3-
40 c θ
41 θ
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43 X, X, ( Y ( Y X X, A ( X X /, B ( Y Y / X X.5, Y Y.5, C ( X, Y X X A, Y Y B, C C C α ( Y Y ( X / X X X, Y Y, E α. 5 ( X, Y E > Y Y, E E X X, E E α X X
44 {( Y Y /( X X } (/ ( X X ( Y Y ( X X ( Y ( X Y X α ( Y Y, β ( X X X X, Y Y, E α ( X X ( X, Y E > Y Y, E E β X X, E E α X X / h, h / α < α < / {( }/( / α < {( }/{( } X, X, ( Y ( Y
45 ( α X X, Y Y ( X, Y X X X X ( < α < / ( X X, ( Y Y X X, Y Y,, X X {( }/( ( X, Y ( X X X, Y X X X X X X, Y Y,, X X ( X, (, X ( / α < ' ( X X, ( Y Y, X X, Y Y,, X ' X {( }/( ( X, Y ( X X, X Y X X X X X X X X, Y Y X X,, X X ' ( X, X (, X ( α X X, Y Y X, Y X X, Y Y ( X X Y X X X X 4- ( < α < /
46 Y X X X 4- ( / α < / / / ( <...(4 α < α < / {( }/( ( < ( ( <...(4 ( <...(4 3
47 4...(4 ( (, 5...(4 ( ( ( ( ( ( ( X 6...(4 ( ( X X 8...(4, 7...(4 ( ( ( ( } {( > < X X X > 9...(4 ( ( X...(4 X X...(4 ( ( ( ( < X...(4 ( X > < < 3...(4 ( ( (,
48 4...(4 ( ( ( X 6...(4..., 5...(4 ( ( ( ( ( } {( X 7...(4 ( < < X 8...(4 ( ( X X 9...(4 ( ( ( ( < X...(4 ( X...(4 (, ( ( (, < < < < α / < α '...(4 ( ' ' ' < }/( {( '
49 3...(4 ( ' ( ' ' < 4...(4 ( ' ' ' < 5...(4 ( (, ' X 6...(4 ( ' ' X X 8...(4, 7...(4 ( ( ( ( } {( ' ' ' ' ' ' ' ' < X X X < 9...(4 ( ( ' ' X 3...(4 X ' ' ' X 3...(4 ( ( ( ( ( ' ' ' ' ' ' X 3...(4 ( ( ' ' X
50 α / α, ', ( ( ' < ' ( ( ' ( < < ' ( < <...(4 33 '... < / / / / it( x x x% y x y
51 4-3
52 it( /, it( / % %????? >? 4-4 /
53 it( /(, it( / %( %???? (?? ( 4-5 /
54 (,, 4-6
55 S 3 S S E Y t E 3 E 5 S 4 Y b E S 5 X l X r E Cohe-Sutherld X X l X X r Y Y b Y Y X X Y t Y b X r X l Y Y t
56 Y Y t Y Y b X X r X X l S E S E X X l X X r X X l X X r Y Y b X X r Y Y b
57 P P P C P C C C C ANDC?? C? C C, P P CAND? CAND? CAND? X X l, P X X Y Y Y t, P r, P Y b, P P C 4-8
58 Y X l X r Y t Y b X X l X r Y t Y b X, X, ( Y ( Y X < X l X > X r X < X l Y > Y t Y < Y b Y ( Y t Yb /
59 Y > Y t S( X, Y Y Y ( X X > ( X X ( Y ( t l Y Y > Y b X < X l X X l X > X r X X r X X r ( Yb Y( X X > ( X l X ( Y Y X X l Y > Y b X X r Y > Y b Y Y b X < X r Y Y b X X r ( Yb Y( X X > ( X r X ( Y Y Y Y b X X r X < X l X X l Y t Y t Y b Y b X l X r 4-4- X l X r
60 X < X l Y < Y b Y > Y t Y ( Y t Yb / Y b < Y < Yt X < X l X X l X > X r X X r Y Y ( X X > ( X X ( Y ( b l Y Y < Y b X < X r Y Y b X X r ( Yb Y( X X > ( X r X ( Y Y Y Y b X X r X < X l X X l Y > Yt Y < Y b X < X l X > X r X l < X < X r Y > Y t Y Y t Y < Y b Y Y < Y < Y b b Y t Y > Y t Y < Y b X < X l X X l
61 ( ( ( ( Y Y X X X X Y Y l t > l X X Y t Y
62 Y Y t X l X r Y b X 4-3 X < X l X > X r Y < Y b Y > Y t X < X l Y < Y b Y > Y t
63 X < X l Y > Y t X < X l Y > Y t Y Y ( X X > ( X X ( Y ( t l Y Y < Y b ( Yb Y( X X > ( X l X ( Y Y X X < X r Y Y b ( Yb Y( X X > ( X r X ( Y Y Y X Y b X r X X l X > X r X X r X > X r ( Yt Y( X X < ( X r X ( Y Y Y Y > Y b X X r ( Yb Y( X X > ( X r X ( Y Y Y X Y b X r Y Y t Y < Y b Y Y b Y t X l
64 X < X l Y < Y b ( Yb Y( X X > ( X l X ( Y Y X X < X r Y < Y b Y Y b Y Y ( X X > ( X X ( Y Y ( b r Y X X r Y b Y > Y t ( Yt Y( X X < ( X l X ( Y Y X X X < X r Y > Y t Y Y t ( Yt Y( X X < ( X r X ( Y Y Y Y t X X r X X l X > X r X X r X X l X X r Y Y b Y Y t ( Yb Y( X X < ( X l X ( Y Y X Y X l Y b ( Yt Y( X X > ( X l X ( Y Y X Y X l Y t X l l
65 ( Yb Y( X X < ( X r X ( Y Y X Y X r Y b ( Yt Y( X X > ( X r X ( Y Y X Y X r Y t
66 l X r X Y b Y t ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS 4-4 Stte l X r X Y b Y t ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS 4-5 Stte
67 l X r X Y b Y t ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS ST NN UCS 4-6 Stte9
68 5-
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111 x b (,,- z - ' b' Y Z - X Y ' b' α
112 b ' b ' α α Z Y u - Y X s ' α b p q b' (,,- r p q o z - t X ( v (b 7-
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114 cos...(7 - si (, / si (,, /, si (cos cos si si, cos si ( si cos si si, cos si (,, ( r for r where r if h r if z y x F, >, θ π η π θ η π φ π θ θ η θ φ θ φ θ θ θ φ θ φ θ X(Y Z h ( (b z X Y r θ ϕ r siθ - 7- θ r θ si...(7 (cos (cos cos η η θ h h z 3...(7 / (( cos h z η π θ η / si ( r 4...(7 / (( cos / si ( h z r η π θ
115 5...(7 / (( cos / ( si h z r π θ X Z -z h(cosη (x,y,z si r θ θ h 7- z h z / (( cos / ( si h z r π θ ( y x ( si y x θ
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121 7-7
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137 x x x x x q r( q r r < x q r q q ( < r < ( r q r x q q ( < r < ( r q x q r x x x x x x x x q r( q r r < x ( q r ( q r ( q q ( < r < ( r q x q r x q x x x x x.,
138 x x x / x x q r( q r r < x q r q < r < x q r q x / ( q r / ( j r / j ( r / ( j ( q x r ( j x / ( q r / ( j r/ j {( r /} ( j q x x x / x q x q r x / ( q r / ( j / j j q x x / ( q r / ( j / j (/ ( j q x x x / x x x / x ( j ( j x x x x q r( q r < r < x ( q r ( q r q x ( x q r q x x
139 x x x x x x x x x x x q r (q r r < x q r (q r r < r r x x ( q r ( q r ( q q ( r r q q q q ( r r ( r r > x ( q ( q q q x x x x x x x x x r r x x ( q r q ( q q r q q x q q q q x ( x x x x x x x x r r x x q ( q r ( q q r q q x q q q q x ( x x x x x x x x r r x x q q q q x q q x x x x x x x x x x x x x x x x x
140 x x x / x q x q r( q r r < x q r x / ( q r / ( j r / j ( r / j q x x / ( q r / ( j r/ j {( r / } j q x x x / x x x x x x x x x x x x q r (q r r < x q r (q r r < x x ( q r ( q r ( q q ( r r q q q q ( r r ( r r < x q q x x x x x x x x x x x x x x q r( q r r < x q r r ( q r ( q r q x x q q x x x x x
141 < α / h < / α h Y b b b z X A- </h</ ( b b h x ( / h x /...( A x h / h / h / z b ( h h / s b h z h /, s h, z ( h h /...( A x x x / x
142 h h / h h h h / h h /...( A 3 s ( h j, j ( h j h / ( j / j h / h / ( h ( h / ( h / h / z ( h h / ( j / j (/ j ( j / ( h / z h / ( h ( h / ( h / h / ( h z...( A 4 h /, s h, z ( h h / s < α / < / Y, z...( A 5 α, z z s X A- </</ x ( / x /...( A 6
143 x /( /( /(...( A 7 x ( / x ( (/...( A 8 ( x...( 9 A {( } ( ( ( x x..( A ( x x z z s z ( (...( A s. ( ( s z....( A, ( (
144 s ( (,...( 3 z A.,., x x x x x x x x x x ( ( x, x x x ( (...( 4 A x x x / x x...( 5 A,...( 6 A ( (...( 7 A, ( (...( A 8 x x x x x x x x x x x (, x x x ( (,
145 9...( ( A / x x x x /...( A ( (,...( ( A ( s (,...( A s x x x x x ( (
146 z (,, 3...( ( A z ( (, z s (, ( 4...(,, A z s. / / < α α, Y X s z z A-3 / / <
147 x 5...( > A x x ( x > ( x,, 6...( ( A x 7...( ( > A x x ( ( x > 8...( ( ( A x.,, ( ( ( ( ( ( ( } {( x x 9...(... A
148 s z x ( } {( x z. 3...( ( } {( ( } {( A z s ( ( } {( z s 3...( ( } {( ( A ( ( ( (, ( 3...( ( } {(, ( } {( ( A z s x x x x x x x x x x ( (, ( ( x x x x ( ( ( ( (
149 33...( ( ( ( ( A / x x x x / x (, 34...( ( A 35...( ( A ( ( ( ( ( ( 36...(... A ( ( ( (, (, 37...( A ( ( ( x x x x ( x ( ( ( ( ( } {( (
150 38...( ( ( } {( ( A ( ( } {( ( ( ( ( } {( ( ( s ( } {( (, ( 39...( A s ( ( } {( ( ( ( } {( ( ( } {(, ( z 4...( A z ( ( ( (, ( ( } {(, ( } {( ( z s 4...(,, A z s.
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63 6 6.1 6.1.1 v = v 0 =v 0x,v 0y, 0) t =0 x 0,y 0, 0) t x x 0 + v 0x t v x v 0x = y = y 0 + v 0y t, v = v y = v 0y 6.1) z 0 0 v z yv z zv y zv x xv z xv y yv x = 0 0 x 0 v 0y y 0 v 0x 6.) 6.) 6.1) 6.)
More informationF = 0 F α, β F = t 2 + at + b (t α)(t β) = t 2 (α + β)t + αβ G : α + β = a, αβ = b F = 0 F (t) = 0 t α, β G t F = 0 α, β G. α β a b α β α β a b (α β)
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More information#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 =
#A A A. F, F d F P + F P = d P F, F P F F A. α, 0, α, 0 α > 0, + α +, α + d + α + + α + = d d F, F 0 < α < d + α + = d α + + α + = d d α + + α + d α + = d 4 4d α + = d 4 8d + 6 http://mth.cs.kitmi-it.c.jp/
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1 ( 12 11 44 7 20 10 10 1 1 ( ( 2 10 46 11 10 10 5 8 3 2 6 9 47 2 3 48 4 2 2 ( 97 12 ) 97 12 -Spencer modulus moduli (modulus of elasticity) modulus (le) module modulus module 4 b θ a q φ p 1: 3 (le) module
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26 12 1 23. xyz ϕ f(x, y, z) Φ F (x, y, z) = F (x, y, z) G(x, y, z) rot(grad ϕ) rot(grad f) H(x, y, z) div(rot Φ) div(rot F ) (x, y, z) rot(grad f) = rot f x f y f z = (f z ) y (f y ) z (f x ) z (f z )
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More informationz f(z) f(z) x, y, u, v, r, θ r > 0 z = x + iy, f = u + iv C γ D f(z) f(z) D f(z) f(z) z, Rm z, z 1.1 z = x + iy = re iθ = r (cos θ + i sin θ) z = x iy
f f x, y, u, v, r, θ r > = x + iy, f = u + iv C γ D f f D f f, Rm,. = x + iy = re iθ = r cos θ + i sin θ = x iy = re iθ = r cos θ i sin θ x = + = Re, y = = Im i r = = = x + y θ = arg = arctan y x e i =
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3-1 ( sit ) (stead state vibratio) (trasiet vibratio) sit(a)w s ( W s ) W / g C (b) sit ( + s ) ( + s ) c + W + sit W s si t + s + c + si t (3.1) si t (3.1) a C W b sit(respose) () 3- acost+ bsit a sit+
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