Issue 53

I. Monetto et alii, Frattura ed Integrità Strutturale, 53 (2020) 372-393; DOI: 10.3221/IGF-ESIS.53.29

constants. Similar considerations are valid for matching based on the other root rotation compliance coefficients 0 M d and 0 N d , under moment and normal force, but explicit expressions for 0 M w k and 0 N w k cannot be derived from Eqns. (22) and (24) together with Eqns. (20) and (21). The pertinent numerical results are listed in Tabs. 1 and 3 for isotropic specimens and in Tabs. 4 and 6 for degenerate orthotropic specimens with  =0.5 (  =1).

0 V d

0 M d

0 N d

0 V c

0 N c

k w





0

2.604 4.474 7.120 2.601 4.451 7.049 2.590 4.358 6.776 2.598 4.205 6.277

3.036

2.043 1.559 1.236 2.061 1.576 1.252 2.137 1.647 1.321 2.332 1.833 1.500

1.518 1.158 0.918 1.376 1.052 0.836 1.258 0.970 0.778 1.178 0.926 0.758

1

0.3 0.5 0.3 0.5 0.3 0.5 0.3 0.5 0 0 0

2.316 16.153 8.077

1.836 2.751 1.671 2.515 1.555 2.355 1.851 1.515

0.8

2.103 13.109 6.554

0.6

1.939 10.440 5.220

0.4

8.151

4.075

0 V d based matching for isotropic materials (  =  =1).

Table 2: Numerical results according to the Timoshenko beam based model and

0 V d

0 M d

0 N d

0 V c

0 N c

k w





0

2.638 4.551 7.275 3.864 7.604

3.016 2.296 1.816 2.257 1.609 1.177 1.607 1.031 0.647 1.097 0.593 0.257

2.026 1.543 1.220 1.604 1.143 0.836 1.217 0.781 0.490 0.901 0.487 0.211

1.508 1.148 0.908 1.128 0.804 0.588 0.803 0.515 0.323 0.549 0.297 0.129

1

0.3 0.5 0.3 0.5 0.3 0.5 0.3 0.5 0 0 0

16.124

8.062

0.8

12.432

6.216

14.212 6.345 15.418 39.156 11.966 40.932 217.687

0.6

9.310

4.655

0.4

6.762

3.381

0 N d based matching for isotropic materials (  =  =1).

Table 3: Numerical results according to the Timoshenko beam based model and

0 V d

0 M d

0 N d

0 V c

0 N c

k w





0

2.603 4.294

3.437 2.147

1

0.3 0.5 0.3 0.5 0.3 0.5 0.3 0.5 0 0 0

3.757 3.574 19.210 9.605 2.861 1.787

5.013 3.094 2.458 4.002 4.610 2.922 1.988 4.060 3.409 3.100 1.309 4.692

2.477 1.547 3.595 2.001 2.625 1.461 4.264 2.030 3.256 1.550 6.148 2.346

0.8

3.499 3.354 15.714 7.857 3.013 1.677

0.6

2.699 3.484 12.904 6.452 3.659 1.742

0.4

1.643 4.188 10.787 5.394 5.488 2.094

1.942 3.852

5.048 1.926

0 M d based matching for orthotropic materials with

Table 4: Numerical results according to the Timoshenko beam based model and

 =1 and  =0.5.

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