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Table 2 Example single patch: first and second order derivatives of the shape functions \(N_i(\xi ,\eta )\) evaluated on the quadrature point p10 (see Fig. 21) with the parameters \(\xi =1.2679\) and \(\eta =0.8452\) (see Listing 10)

From: Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis

\(cp\ id\) \(\frac{\partial N}{\partial \xi }\) \(\frac{\partial N}{\partial \eta }\) \(\frac{\partial N}{\partial \xi ^2}\) \(\frac{\partial N}{\partial \eta ^2}\) \(\frac{\partial N}{\partial \xi \cdot \partial \eta }\)
1 \(-\) 0.16352 \(-\) 0.24528 0.03455 0.07775 0.10366
2 0.11970 \(-\) 0.13144 \(-\) 0.06911 0.04166 \(-\) 0.07589
3 0.04381 \(-\) 0.01761 0.03455 0.00558 \(-\) 0.02777
4 \(-\) 0.08763 0.17955 0.01851 \(-\) 0.15550 \(-\) 0.07589
5 0.06415 0.09622 \(-\) 0.03703 \(-\) 0.08333 0.05555
6 0.02348 0.01289 0.01851 \(-\) 0.01116 0.02033
7 \(-\) 0.01174 0.06572 0.00248 0.07775 \(-\) 0.02777
8 0.00859 0.03522 \(-\) 0.00496 0.04166 0.02033
9 0.003145 0.004718 0.002481 0.005582 0.007443