Issue 53

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