Issue 59

H.A. Mobaraki et alii, Frattura ed Integrità Strutturale, 59 (2022) 198-211; DOI: 10.3221/IGF-ESIS.59.15







 





   x y ,

 

 



    x y ,

B

0, u v y

D

D

2 2

2

2

, y x

x

, y y x x

, y x x x ,

66

0,

12 ,

16





 





    x y ,



 A w 





D

w

2

] dy dx

, y x y y ,

x

x

y

y

26

45

0,

0,

Furthermore, the kinetic energy of the laminated composite plate is:

  0 0 1 [ ( a b 0

   I





  2 I u v w I u 2 ) + 2

2 ,t

   2 2



   v

(6)

T

dy dx

P

t

t

, 1 t x t ,

t

, y t

, 2 x t

, y t

,

,

,

2

where 

 0 1 2 , , I I I are mass moments of inertia, defined as follows:

  



    h h

 2





2



I I I

1, , z z z dz

(7)

0 1 2 , ,

2

As mentioned earlier, a moving vehicle is modeled with 3-DOF as shown in Fig. 1. The potential energy of the vehicle is:

1 2

1 2









2

2

 U k q w b q a q    2 V V V 1 1 1



   k q w b q a q 2 1 2 2 V V

3

3

(8)

mg

1 2

1 2













2

2



   k q w b q a q 3 1 3 2 V V



   k q w b q a q 4 1 4 2 V V



   w w w w

3

3

1

2

3

4

4

where









 i i w w x y 0 , i



i

1, 2, 3, 4

(9)

Also, the damped energy of dashpots can be written as:

1 2 1 2

1 2









2

2

 W c q w b q a q        1 1 1 2 V V dv



   c q w b q a q     2 1 2 2 V V

3

3

(10)

1 2









2

2



   c q w b q a q     3 1 3 2 V V



   c q w b q a q     4 1 4 2 V V

3

3

i k and  i c i



 1, 2, 3, 4

In the above equations,

refer to the suspension system stiffness and damping parameters,

respectively. Moreover, the kinetic energy of the vehicle is:

1 2

1 2

1 2

  2

2

2



(11)

 T mq V

 I q x

 I q y

1

2

3

where m is the vehicle total mass and x I and y I are its mass moments of inertia about the x - and y -axes respectively.

Figure 2: Rectangular higher-order element

201