Issue 52

N. Hebbar et alii, Frattura ed Integrità Strutturale, 52 (2020) 230-246; DOI: 10.3221/IGF-ESIS.52.18

power-law p since the dimensionless displacement increases as the index of the power-law increases and precisely in the two upper and lower parts of the beam.

L/h=5

L/h=20

Theory

u

w

u

w

p

x 

x 

xz 

xz 

0.8569 0.9397

2.9063 3.1654

3.8071 0.7325 0.2098 3.8019 0.7332 0.2306

2.6372 15.0143 0.7455 2.8962 15.0129 0.7437

Present ( ε z  0) Present ( ε z =0) Hadji et al. [25]

0

0.9400 3.1654 3.8019 0.7330 0.2305 2.8962 15.0129 0.7437 0.9274 3.1224 3.7529 0.7259 0.2275 2.8585 14.8179 0.7259 0.9397 3.1654 3.8019 0.7330 0.2306 2.8962 15.0129 0.7437

A.S. Sayyad and Y.M.Ghugal [58]

Reddy [11]

2.0993 2.3038 2.3038 2.2735

5.7397 6.2594 6.2594 6.2586

5.8924 0.7325 0.5174 5.8835 0.7330 0.5685 5.8835 0.7330 0.5685 5.8077 0.7187 0.5611

5.2852 23.2076 0.7455 5.8049 23.2051 0.7437 5.8049 23.2051 0.7437 5.7292 22.9038 0.7259

Present ( ε z  0) Present ( ε z =0) Hadji et al. [25]

1

A.S. Sayyad and Y.M.Ghugal [58]

Reddy [11]

2.3036 6.2594 5.8836 0.7330 0.5686 5.5685 23.2051 0.7432 2.8363 7.4016 6.8940 0.6699 0.6999 6.7760 27.1021 0.6828 3.1129 8.0677 6.8824 0.6704 0.7366 7.2558 27.0989 0.6812 3.1129 8.0677 6.8824 0.6704 0.7366 7.2558 27.0989 0.6812 3.0720 7.9627 6.7938 0.6573 0.7591 7.3450 26.7470 0.6648

Present ( ε z  0) Present ( ε z =0) Hadji et al. [25]

2

A.S. Sayyad and Y.M.Ghugal [58]

Reddy [11]

3.1127 3.3815 3.7100 3.7100

8.0677 9.0403 9.8281 9.8281

6.8824 0.6704 0.7691 8.1272 0.5898 0.8313 8.1104 0.5904 0.9134 8.1104 0.5904 0.9134

7.4421 27.0989 0.6812

8.0.06

31.8173 0.6025

Present ( ε z  0) Present ( ε z =0) Hadji et al. [25]

5

8.8182 32.8127 0.6013 8.8182 32.8127 0.6013

A.S. Sayyad and Y.M.Ghugal [58]

3.6612 9.6986 8.0059 0.5786 0.9014 8.7031 31.3997 0.5863 3.7097 9.8281 8.1104 0.5904 0.9134 8.8182 31.8127 0.6013 3.5434 10.0733 9.7310 0.6459 0.8679 8.8259 38.1434 0.6599 3.7462 10.9381 9.7123 0.6467 0.9536 9.6905 38.1387 0.6600

Reddy [11]

Present ( ε z  0) Present ( ε z =0) Hadji et al. [25]

10

3.8863 3.8351 3.8859

10.9381 9.9878 0.7064 0.9262 10.7949 9.5870 0.6412 0.9412 10.9381 9.7119 0.6465 0.9536

9.5513 38.1382 0.6586 9.5641 37.6432 0.6426 9.6905 38.1382 0.6586

A.S. Sayyad and Y.M.Ghugal [58]

Reddy [11]

Table 2: Comparison of the dimensionless displacements and stress of the FG beams subjected to uniformly distributed load with various power-law exponent values.

4

p=0 p=1 p=2 p=5 p=10

3

2

1

0

-1

-2

Axial displacement (u)

-3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 -4

x/L

Figure 5: Variation of dimensionless axial displacement (u) along the length of the beam subjected to uniformly distributed load with a ratio (L/h=5).

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