Issue 64

M. A. Kenanda et alii, Frattura ed Integrità Strutturale, 64 (2023) 266-282; DOI: 10.3221/IGF-ESIS.64.18

   T Δ = U ,V ,W ,

    x y z mn mn mn mn mn mn , ,

(13b)

The coefficients of matrices [S] and [m] can be deduced as:





2

2

11 33 S =-A λ -A μ , 11

12 33 S =- λμ A +A 33 S =-V λ -V μ 12 2 2 14 11





3

2

13 33 S =B λ + λμ B +2B , 11 12





15 33 S =- λμ V +V , 22 S =-A λ -A μ , 33 S =- λμ V+V , 12 2 2 22 33   24 12

16 11 S =D λ





3

2

23 33 S =B μ + λ μ B +2B 22 12

2

2

25 22 S =-V λ -V μ 33

(14a)





4 2 2 22 S =-E λ - λ μ 2E +4E -E μ 33 11 12 33

4

26 12 S =D μ ,









3

2

3

2

34 33 S =F λ + λμ F +2F , 11 12

35 33 S =F μ + λ μ F +2F 33 S =-M -H λ -H μ 22 12 2 2 44 44 11

2

2

36 12 S =-G λ -G μ , 33 S =- λμ H +H , 11   45 12

 



46 S = λ K -M S = μ K -M 11

44



2

2

55 22 S =-M -H λ -H μ , 55 S =-L -M λ -M μ 55 33 7 2 66 11 44

56

12

55

11 22 1 m =m =D ,

13 2 m =- λ D ,

14 25 4 m =m =D ,

23 2 m =- μ D





2

2

33 1 3 m =D +D λ + μ ,

34 5 m =- λ D ,

35 5 m =- μ D

(14b)

36 7 m =D ,

44 55 6 m =m =D ,

66 8 m =D

12 45 56 m=m=m=m=m=m=m=m=0 15 16 24 26 46

ij ij ij ij A ,B ,V ,D ,E ,F ,G ,K ,L ) are indicated in Appendix B. ij

where the stiffness coefficients ( ij ij ij ij

R ESULTS AND DISCUSSION

F

rom the previous theoretical development, this section examines the competence and accuracy of the above mentioned theory (see Tab. 1) in comparison with popular benchmark linear analysis. This part is divided into four basic examples for confirming the correctness and effectiveness of the current theory and for studying, in particular, the influence of certain parameters such as the power-law index and the effect of geometric and material properties (the effect of the (a/b) and (a/h) ratios, etc.).The material properties and non-dimensional parameters are defined as follows:  Material properties: The properties of aluminum (AL) are: ρ 3 m m m E =70GPa; =2702kg/m ; ν =0.3 The properties of alumina ( 2 3 AL O ) are: ρ 3 c c c E =380GPa; =3800kg/m ; ν =0.3 The properties of zirconia ( 2 ZrO ) are: ρ 3 c c c E =200GPa; =5700kg/m ; ν =0.3  Boundary conditions: x x x yz z y z y y y xz z x z N =v=w=M =S =Q =N = θ = θ =0 at x=0 N =u=w=M =S =Q =N = θ = θ =0 at y=0  Non-dimensional parameters: ρ ρ ρ ρ   2 c m m c m m a ˆ ω = ω h , ω = ω h , ω = ω h , ω = ω G E E h E

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