 MỤC LỤC
CHƯƠNG 1: TỔNG QUAN 1
1.1.  1
  6
1.3.   8
1.4.  9
1.5.   10
CHƯƠNG 2: LÝ THUYẾT CƠ HỌC RẠN NỨT, LÝ THUYẾT ĐÀN HỒI,
LÝ THUYẾT TẤM 11
2.1.  11
2.2.  17
 21
CHƯƠNG 3: PHƯƠNG PHÁP PHẦN TỬ HỮU HẠN 26
3.1.  26
3.2.  giác 8 nút 28
 30
3.4.  trong FEM 33
3.5.  34
3.6.  35
 37
-  38
3.9. PNewmark 40




liên  
  .
 thái mà


 
   


 
- 1933) 

 
       
     


 




Chương 1
GVHD: PGS.TS Nguy2




Chương 1
GVHD: PGS.TS Nguy3


tr, Fracture
Mechanics).
V

        rwin, David Broeke Paris

 [4, 32]








Richard W. Hertzberg. Cơ học biến dạng và rạn nứt của vật liệu cơ khí”
[36].
Irwin, G.R.“Động học rạn nứt”, “Sự rạn nứt của vật liệu” [18]





 


nứt elip dưới ứng suất kéo” [7].
Chongmin Song*, Zora Vrcelj. “Đánh giá hệ số cường độ và ứng suất T
bằng phương pháp điều kiện biên” 
-
i nghiên

CTOD – crack tip open displacement
(độ mở đầu vết nứt) .

 J integral.
Cá



  Khiêm  
 

Chương 1
GVHD: PGS.TS Nguy5
   
.
 
Xuân Hoàng -  
.
               
khung   
  


             
 
,  v.v
 


   
          
 v.v 
 v.v


               

 v.v





.
V
  , 
tài :
Phân tích           
.

1.2  .




 
    -1783)      


Daniel Bernoulli Euler







 
 
Chương 1
GVHD: PGS.TS Nguy8


 nhà 
Sophie Germaine (1776-
.
             

        
1811 [31].

1.3  .


p
               




p


                
Reissner- 
[1, 38].

1.4  (PTHH)
      Finite element method)
  
               o hàm


Phần tử hữu hạn (Finite element) ình
 1960. 



 

O. C Zienkiewicz, R. L. Taylor (1967, 1971, 1977, 1989), G. Strang, G.
Fix (1973), J. N. Reddy (1984, 1993), S. S. Rao (1982, 1989), T. J. T. Hughes
(1979), R. H Gallagher (1975), E. L. Wilson (1971)
Chương 1

 
Chương 2: 
 Trang 11

C
 

2.1. 

 


xác, l [20, 22, 23].

2.1.1  [50]
Kh  hình thành 
 
 n. 
 
.  là
Hình 2.1a

  
, Hình 2.1b              
  


 












 

Phá



Phá

Hình 2.1: nh hưởng của vết nứt đến tần số và độ bền
kết ấ
a)
b)
Chương 2: 
 Trang 13

 
, Hình 2.3
Hình 2.3: Vết nứt trong trường hợp ứng suất kéo

3
cos.
2
cos.
2
sin.
2
.
2
3
sin.
2
sin1.
2
cos.
2
.
2
3
sin.
2
sin1.
2
cos.
2
.



















2
3
cos.
2
cos.
2
sin.
2
2
3
sin.
2
sin1.
2
cos.
2

Ch


d
x

d
y

2a

y


x

r
y
x

xy

Chương 2: 
 Trang 14







sin21.
2
cos.
2
.
2
2
sin21.
2
cos.
2
.
2
2
1
2
1








r
G
K
u
r


,
0
xy

(2.4)
hình thành  II III, 
  là:





























r
K
r
K
r
K
II
xy
II
y
II
x
(2.5)












2
cos21.
2
sin.
2
.
2
2
2








r
G
K
u
r
G
K
u
II
y
II
x
(2.6)




r
K
u
r
K
r
K
III
z
III
yz
III
xz
(2.7)

K
I
, K
II
, K
III
n u III III


lúc thì:
Chương 2: 
 Trang 15

ij


(2.10)

I
= K
IC

 K
IC
          (Critical Stress Intensity
Factor)
2.hình thành  [50]

     
  
.
              
th, t

= 0,

ch
p
y
r
K



            ; a là
 ;

ch
.
đàn – dẻo, 


*
p
r

y


ch


               
*
2
pp
rr 
[18, 37], Hình 2.4
Chương 2: 
 Trang 16
 Hình 2.4: Vùng biến dạng dẻo tại đáy vết nứt Hình 2.5: Độ mở rộng của đáy vết nứt

E
COD
p


(2.13)
2.1.4 (Stress Intensity Factor) [17, 50]
 h
 . 
:

)2(lim
0
rK
r



(2.14)
Hình 2.3 và  

0

 K
hình 
.  K



aK

r

Chương 2: 
 Trang 17


 



 K
C
. , K
C



C
KK 
(2.16)
K
C

 
hình 
 (2.14

 [36, 40]:



,,,,,
      o
x, y, z z, x, y.
   
xzyzxyxxx

,,,,,
      
x, y, z  z, x, y.

              
3D  c  thành phân tích
2D [12].
z 
, Oxy, Hình 2.7,

N
0
yzxzz

(2.18)
z  (
0
z

). 
.
a. Quan hệ ứng suất - biến dạng – nhiệt độ
Hình 2.7: Mô hình bài toán ứng suất phẳng
Hình 2.6: Các thành phần ứng suất và biến dạng




















0
0
0
.
/100
0/1/
0//1
xy
y
x
xy


 
0

là vector 
][

; E ;  
:
)1(2



E
G
(2.21)
 
 (2.19:




























0
0
0
2
.
2/)1(00
01
01
1
xy
y
x
xy
y
x


.

 
0

:
























u
xyyx













; ;
(2.25)

















(2.26)
Chương 2: 
 Trang 20

Hay
   
uD][

(2.27)

c. Phương trình cân bằng

















u
      S
t
[13    S
u
ta có
00
, vvuu 
và trên S
t
ta có
00
,
yyxx
tttt 

yx
tt ,
o 
x, y 
0000
,,,
yx
ttvu

2.3. 
       




2/



h
h
xx
zdzM

;

2/
2/



h
h
yy
zdzM

;



2/
2/
h
h
xyxy

(2.29)
2.3.2. 
Kirchhoff [1, 9, 12]:
- 

- 
hòa.
- 
a. - - 
t, Hình 2.10
Hình 2.9: a) Các thành phần lực và Momen trên tấm; b) Sự phân bố ứng suất
a)
b)
Chương 2: 
 Trang 22


.
y
x
w
u z z
x
w
v z z
y



  

w
z
x
u
x





















2
xy
2
2

















xy
y
x
xy
y
x
E






















xy
y
x
xy
y
x
k
k
k
E
z
2/)1(00
01
01
1
2









2
2
2
2
2
2,,,,
(2.34)
E  isson
{k}
b. :

Ngàm:
0 ,0 



n
w
w