Chap01
24
Logan 의 유한요소법 첫걸음 (신종계, 이용신, 조성욱) 제 1 장: 서 론 A First Course in the Finite Element Method by Daryl L. Logan Page 01-1 제 1 장 서론 유한요소법은 공학과 수리 물리학의 문제들을 풀기 위한 하나의 수치 기법이다. - 구조 해석, 열전달, 유동장, 물질 이동, 그리고 전자기장 해석 등이다. - 복잡한 기하학적 형상과 하중 그리고 재료 - 해석적인 수학해를 구하는 것은 불가 - 물체를 더 작은 물체나 단위(유한요소)로 나누고, 그 요소들을 두 개 이상의 요소들이 공유 하는 점(절점)이나, 경계선, 또는 경계면으로 연결된 대등한 시스템으로 만드는 모델화 과정 을 이산화(discretization) 혹은 격자분할이라고 한다. 유한요소법에서는 전체 물체에 대한 문제를 한 번에 풀지 않고, 각각의 유한요소에 대한 방정식을 세우고, 그들을 조합하여 전체 물체에 대한 방정식을 구한다.
description
soulution
Transcript of Chap01
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Logan (, , ) 1 :
A First Course in the Finite Element Method by Daryl L. Logan Page 01-1
1 . - , , , , .
- -
- () ,
(), ,
(discretization) .
, ,
.
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Logan (, , ) 1 :
A First Course in the Finite Element Method by Daryl L. Logan Page 01-2
1.1 - 1940
Hrennikoff[1], McHenry[2] ; (1 ) Courant[3] ; (piecewise) ( ) Levy[4] ;
- 1950
Levy[5] ; .
Argyris Kelsey[6,7] Turner, Clough, Martin, Topp[8] ; 2 - 1960 Clough[9], Topp[8] ; Melosh[10], Grafton Strome[11], Martin[12], Gallagher, Padlog, Bijlaard[13], Melosh[14], Argyris[15], Clough Rashid[16], Wilson[17] ,Turner, Dill, Martin, Melosh [18], Gallagher, Padlog, Bijlaard [13]. Gallagher Padlog[19] Zienkiewicz, Watson, King[20], Archer[21], Melosh[14] () : Zienkiewicz Cheung[22], Martin[23], Wilson Nickel[24] - 1970
Zienkiewicz Parekh[26] (transient field problem) - .
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1.2
- , - : (column matrix)
F F
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# # (1.2.1)
A First Course in the Finite Element Method by Daryl L. Logan Page 01-3
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[ ]
11 12 1
21 22 2
1 2
n
n
n n nn
k k kk k k
k k
k k k
= =
""
# # #"
[ ]
11 12 1
21 22 2
1 2
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n n nn
K K KK K K
K K
K K K
= =
""
# # #"
; kij Kij (stiffness influence coefficients)
F Kd= (1.2.4)
A First Course in the Finite Element Method by Daryl L. Logan Page 01-4
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A First Course in the Finite Element Method by Daryl L. Logan Page 01-5
1.3
- .
- . ---> ---> ,
,
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A First Course in the Finite Element Method by Daryl L. Logan Page 01-6
1.4
1. ; (internal force)
2. ;
[34] , () .
(finite element) . . . () .
. < , , , > < , , 3 > < , >
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1:
(a)
(b) / 2
A First Course in the Finite Element Method by Daryl L. Logan Page 01-7
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(c) 3 3
(d)
1.1:
A First Course in the Finite Element Method by Daryl L. Logan Page 01-8
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2: : 2 2 ( , ) x y-
(2 , x ) . y 3: -, - - : 1, x
xdudx
= (1.4.1) - : (Hooke)
x xE = (1.4.2)
A First Course in the Finite Element Method by Daryl L. Logan Page 01-9
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A First Course in the Finite Element Method by Daryl L. Logan Page 01-10
4: (Direct Equilibrium Method) - - . - 1 2, 3, 5 ,
- 2 3 . - (virtual work) , , (Castigliano)
(Method of Weighted Residuals)
- (functional) . - . -
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A First Course in the Finite Element Method by Daryl L. Logan Page 01-11
"""
# # #"
# (1.4.3)
1 11 12 13 1 1
2 21 22 23 2 2
3 31 32 33 3 3
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n
n
n
n n nn n
f k k k k df k k k k df k k k k d
f k k d
=
{ } [ ] { }f k d= (1.4.4) , fk p k ,
, (generalized) .
dk p n
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5: .
{ } [ ] { }F K d= (1.4.5) , Fk p K ,
. dk p , K (determinant) 0 .
( )
A First Course in the Finite Element Method by Daryl L. Logan Page 01-12
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6: ( )
A First Course in the Finite Element Method by Daryl L. Logan Page 01-13
# #
1 11 12 1 1
2 21 22 2 2
1 2
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n
n n n nn n
F K K K dF K K K d
F K K K d
= (1.4.6)
(Gauss) - . d 7: 8: (postprocessor) .
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A First Course in the Finite Element Method by Daryl L. Logan Page 01-14
1.5
1. , , , 2. 3.
.
1. 2. , (seepage) 3.
1. 2. 3. 4. , 5. 6.
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1.2: (28 , 48 )
A First Course in the Finite Element Method by Daryl L. Logan Page 01-15
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1.3: (369 , 40 , 333
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A First Course in the Finite Element Method by Daryl L. Logan Page 01-16
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1.4: 2 (120 , 297 )
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1.5: (45 )(584 , 252
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1.6: (240 )[40]
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1.7: (backhoe) (swing casting) 3
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1.8: 2
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1.9: ( 5000
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1.6
1. .
2. .
3.
.
4. , .
5. .
6. .
7. .
8. . , ,
, , , , , ( [22, 23, 24, 27, 42, 43, 44] ).
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A First Course in the Finite Element Method by Daryl L. Logan Page 01-24
1.7 .
1. . 2. . 3. , . 4. . 5.
.
1. . 2. . 3. . 4. ( ).
1. ALGOR [46] 2. ANSYS [47] 3. GIFTS [48] 4. IMAGES-3D [49] 5. MSC/PAL [50] 6. TAB/SAP86 [51]
