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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