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Logan (, , ) 1 :
A First Course in the Finite Element Method by Daryl L. Logan Page 01-1
1 . - , , , , .
- -
- () ,
(), ,
(discretization) .
, ,
.
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) - .
Logan (, , ) 1 :
1.2
- , - : (column matrix)
F F
FFFFFF
FFF
d d
dddddd
ddd
x
y
z
x
y
z
nx
ny
nz
x
y
z
x
y
z
nx
ny
nz
l q l q= =
R
S
|||||||
T
|||||||
U
V
|||||||
W
|||||||
= =
R
S
|||||||
T
|||||||
U
V
|||||||
W
|||||||
1
1
1
2
2
2
1
1
1
2
2
2
# # (1.2.1)
A First Course in the Finite Element Method by Daryl L. Logan Page 01-3
Logan (, , ) 1 :
[ ]
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
n
n
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
Logan (, , ) 1 :
A First Course in the Finite Element Method by Daryl L. Logan Page 01-5
1.3
- .
- . ---> ---> ,
,
Logan (, , ) 1 :
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 > < , >
Logan (, , ) 1 :
1:
(a)
(b) / 2
A First Course in the Finite Element Method by Daryl L. Logan Page 01-7
Logan (, , ) 1 :
(c) 3 3
(d)
1.1:
A First Course in the Finite Element Method by Daryl L. Logan Page 01-8
Logan (, , ) 1 :
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
Logan (, , ) 1 :
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) . - . -
Logan (, , ) 1 :
.
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
1
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
Logan (, , ) 1 :
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
Logan (, , ) 1 :
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
n
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) .
Logan (, , ) 1 :
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.
Logan (, , ) 1 :
1.2: (28 , 48 )
A First Course in the Finite Element Method by Daryl L. Logan Page 01-15
Logan (, , ) 1 :
1.3: (369 , 40 , 333
)[39]
A First Course in the Finite Element Method by Daryl L. Logan Page 01-16
Logan (, , ) 1 :
1.4: 2 (120 , 297 )
A First Course in the Finite Element Method by Daryl L. Logan Page 01-17
Logan (, , ) 1 :
1.5: (45 )(584 , 252
)
A First Course in the Finite Element Method by Daryl L. Logan Page 01-18
Logan (, , ) 1 :
1.6: (240 )[40]
A First Course in the Finite Element Method by Daryl L. Logan Page 01-19
Logan (, , ) 1 :
1.7: (backhoe) (swing casting) 3
A First Course in the Finite Element Method by Daryl L. Logan Page 01-20
Logan (, , ) 1 :
1.8: 2
A First Course in the Finite Element Method by Daryl L. Logan Page 01-21
Logan (, , ) 1 :
1.9: ( 5000
)[41]
A First Course in the Finite Element Method by Daryl L. Logan Page 01-22
Logan (, , ) 1 :
A First Course in the Finite Element Method by Daryl L. Logan Page 01-23
1.6
1. .
2. .
3.
.
4. , .
5. .
6. .
7. .
8. . , ,
, , , , , ( [22, 23, 24, 27, 42, 43, 44] ).
Logan (, , ) 1 :
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]
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