Issue 53

I. Monetto et alii, Frattura ed Integrità Strutturale, 53 (2020) 372-393; DOI: 10.3221/IGF-ESIS.53.29 390 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).   k w 0 V d 0 M d 0 N d 0 V c 0 N c 0 2.604 3.036 2.043 1.518 1 0.3 4.474 2.316 16.153 8.077 1.559 1.158 0.5 7.120 1.836 1.236 0.918 0 2.601 2.751 2.061 1.376 0.8 0.3 4.451 2.103 13.109 6.554 1.576 1.052 0.5 7.049 1.671 1.252 0.836 0 2.590 2.515 2.137 1.258 0.6 0.3 4.358 1.939 10.440 5.220 1.647 0.970 0.5 6.776 1.555 1.321 0.778 0 2.598 2.355 2.332 1.178 0.4 0.3 4.205 1.851 8.151 4.075 1.833 0.926 0.5 6.277 1.515 1.500 0.758 Table 2: Numerical results according to the Timoshenko beam based model and 0 V d based matching for isotropic materials (  =  =1).   k w 0 V d 0 M d 0 N d 0 V c 0 N c 0 2.638 3.016 2.026 1.508 1 0.3 4.551 2.296 16.124 8.062 1.543 1.148 0.5 7.275 1.816 1.220 0.908 0 3.864 2.257 1.604 1.128 0.8 0.3 7.604 1.609 12.432 6.216 1.143 0.804 0.5 14.212 1.177 0.836 0.588 0 6.345 1.607 1.217 0.803 0.6 0.3 15.418 1.031 9.310 4.655 0.781 0.515 0.5 39.156 0.647 0.490 0.323 0 11.966 1.097 0.901 0.549 0.4 0.3 40.932 0.593 6.762 3.381 0.487 0.297 0.5 217.687 0.257 0.211 0.129 Table 3: Numerical results according to the Timoshenko beam based model and 0 N d based matching for isotropic materials (  =  =1).   k w 0 V d 0 M d 0 N d 0 V c 0 N c 0 2.603 4.294 3.437 2.147 1 0.3 3.757 3.574 19.210 9.605 2.861 1.787 0.5 5.013 3.094 2.477 1.547 0 2.458 4.002 3.595 2.001 0.8 0.3 3.499 3.354 15.714 7.857 3.013 1.677 0.5 4.610 2.922 2.625 1.461 0 1.988 4.060 4.264 2.030 0.6 0.3 2.699 3.484 12.904 6.452 3.659 1.742 0.5 3.409 3.100 3.256 1.550 0 1.309 4.692 6.148 2.346 0.4 0.3 1.643 4.188 10.787 5.394 5.488 2.094 0.5 1.942 3.852 5.048 1.926 Table 4: Numerical results according to the Timoshenko beam based model and 0 M d based matching for orthotropic materials with  =1 and  =0.5.