Issue 53
I. Monetto et alii, Frattura ed Integrità Strutturale, 53 (2020) 372-393; DOI: 10.3221/IGF-ESIS.53.29
0 V d
0 M d
0 N d
0 V c
0 N c
k w
0
2.604 4.294
3.437 2.147
1
0.3 0.5
3.759 3.574 19.210 9.605 2.860 1.787
5.016 3.094 2.601 3.891
2.476 1.547 3.467 1.945
0
0.8
0.3 0.5
3.744 3.243 15.589 7.795 2.889 1.621
4.984 2.811 2.590 3.557
2.504 1.405 3.594 1.778
0
0.6
0.3 0.5
3.688 2.981 12.415 6.208 3.012 1.490
4.859 2.597 2.598 3.331 3.606 2.826 4.465 2.490
2.624 1.298 3.921 1.665
0
0.4
0.3 0.5
9.693
4.846 3.328 1.413
2.932 1.245
0 V d based matching for orthotropic materials with
Table 5: Numerical results according to the Timoshenko beam based model and
=1 and =0.5.
0 V d
0 M d
0 N d
0 V c
0 N c
k w
0
2.638 3.818 5.107 3.864 6.084 8.828 6.345
4.266
3.408 2.133
1
0.3 0.5 0.3 0.5 0.3 0.5 0.3 0.5 0 0 0
3.546 19.175 9.587 2.833 1.773
3.066 3.192 2.112 2.272 1.312 1.552 1.048 0.712
2.449 1.533 2.697 1.596 1.784 1.056 2.047 1.136 1.183 0.656 1.516 0.776
0.8
2.544 14.784 7.392 2.149 1.272
0.6
11.386 19.023 11.966 26.246 56.875
1.696 11.072 5.536 1.528 0.848
0.4
8.041
4.021 1.023 0.524
0.695 0.356
0 N d based matching for orthotropic materials with
Table 6: Numerical results according to the Timoshenko beam based model and
=1 and =0.5.
Matching the compliance coefficients using the Euler-Bernoulli beam based model With reference to the simplified model according to the Euler-Bernoulli beam theory, for matching based on the root rotation compliance coefficient 0 M EB d under moment, the use of the first of Eqn. (25b) leads to the following expression
10
(1 ) 54
0 M EB w
k
(B.2)
4
M M
a
a
0
0
1
2
0 2 M M M a 0 1
0 has been enforced. Substituting Eqn. (B.2) into Eqns. (25a) and (25b) gives the remaining
where
EB d a
compliance coefficients. Similarly, for matching based on the root rotation compliance coefficient 0 N
EB d under normal
force, from the second of Eqn. (25b) we derive
10
(1 ) 27
0 N EB w
k
(B.3)
4
N N
8
a
a
0
0
1
2
391
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