Issue 55

M. M. Konieczny et alii, Frattura ed Integrità Strutturale, 55 (2021) 241-257; DOI: 10.3221/IGF-ESIS.55.18

 

   

   

2

** B d 1

  

  

t r

  C

C C

d

   1 1

 

(5)

2

*

2

*

r dr C

dr

B

r

C B

r

r

r

where the function of the transverse force intensity t(r) for the most common methods of plate support was assumed to take the form [16]:

     2 3 k t r k r k r r 1

2

(6)

where: k 1 , k 2 , k 3 – lateral force function coefficients. The solution to Eqn. (5) is given by the function of the plate deflection angle  ( r ):

  

  

4

3

3 k r

1 k r

2 k r

1

  r

  1 λ D r

λ

2 D r

(7)

2

   3 λ 3 λ

 

   1 λ 1 λ

 

   4 λ 4 λ

1

*

C B

1

2

1

2

1

2

r

in which 1 λ and 2 λ are roots of the characteristic equation:

**

        1 λ r r C C C C   

B

2

λ

0

(8)

*

B

In function (7), which is the general integral of the differential Eqn. (5), the constant coefficients k 1 , k 2 , k 3 depend on the load method, while D 1 and D 2 are integration constants whose numerical values are determined on the basis of the boundary conditions given in this study. After determining the function φ (r) from compounds (2) and (3), the intensities of radial and circumferential moments in the base material (steel) m r1 , m θ 1 and in the plating layer (titanium) m r2 , m θ 2 are determined. The deflection of the bimetallic perforated plate with the plating layer is determined by the relationship:          3 w r r dr D (9) where D 3 – integration constant. The stress in the cross-sections of the bimetalic perforated plate (Fig. 3) is derived on the basis of the compounds: 1) Radial stress  r : a) in the base material of the plate (steel)  1 r :

3 r m

 

, dla    1 2 h z h

z

(10)

 1

r

3

3

C h h

1

r

1

2

b) in the applied layer of the plate (titanium)  2 r :

3 r m

     2 2 h z h a

 

z

, dla

(11)

2

r

    3 3

 

2

C h a h

r

1

2

2) Circumferential stress   : a) in the base material of the plate (steel)

  1 :

3 m

  1

  

z

, dla    1 2 h z h

(12)

3

3

C h h

1

1

2

245

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