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Table 5 Errors for all 14 DOF models, 0/90/0, \(\hbox {R/a} =5, \hbox {a/h} = 5\)

From: Best theory diagrams for multilayered structures via shell finite elements

\({\varvec{R/a}} = 100\)

\({\varvec{R/a}} = 10\)

\({\varvec{R/a}} = 5\)

Inactive

Inactive

Inactive

DOF

Error (%)

DOF

Error (%)

DOF

Error (%)

\(\hbox {u}_{z5}\)

\(4.1 \times 10^{-6}\)

\(\hbox {u}_{x3}\)

\(9.5 \times 10^{-4}\)

\(\hbox {u}_{x3}\)

\(4.6 \times 10^{-5}\)

\(\hbox {u}_{z4}\)

\(1.5 \times 10^{-4}\)

\(\hbox {u}_{x5}\)

\(2.1 \times 10^{-3}\)

\(\hbox {u}_{x5}\)

\(3.8 \times 10^{-3}\)

\(\hbox {u}_{x3}\)

\(3.0 \times 10^{-4}\)

\(\hbox {u}_{z4}\)

\(7.3 \times 10^{-3}\)

\(\hbox {u}_{x2}\)

\(5.6 \times 10^{-3}\)

\(\hbox {u}_{x5}\)

\(4.0 \times 10^{-4}\)

\(\hbox {u}_{y5}\)

\(8.5 \times 10^{-3}\)

\(\hbox {u}_{y5}\)

\(9.4 \times 10^{-3}\)

\(\hbox {u}_{y5}\)

\(1.1 \times 10^{-3}\)

\(\hbox {u}_{z5}\)

\(9.0 \times 10^{-3}\)

\(\hbox {u}_{z4}\)

\(9.8 \times 10^{-3}\)

\(\hbox {u}_{y4}\)

\(1.2 \times 10^{-3}\)

\(\hbox {u}_{y3}\)

\(2.6 \times 10^{-2}\)

\(\hbox {u}_{y3}\)

\(4.0 \times 10^{-2}\)

\(\hbox {u}_{x4}\)

\(1.4 \times 10^{-3}\)

\(\hbox {u}_{z2}\)

\(3.6 \times 10^{-2}\)

\(\hbox {u}_{z5}\)

\(6.8 \times 10^{-2}\)

\(\hbox {u}_{y3}\)

\(3.2 \times 10^{-3}\)

\(\hbox {u}_{y4}\)

\(9.2 \times 10^{-2}\)

\(\hbox {u}_{z3}\)

\(2.0 \times 10^{-1}\)

\(\hbox {u}_{z2}\)

\(4.1 \times 10^{-3}\)

\(\hbox {u}_{z3}\)

\(9.6 \times 10^{-2}\)

\(\hbox {u}_{z2}\)

\(2.4 \times 10^{-1}\)

\(\hbox {u}_{z3}\)

\(4.5 \times 10^{-3}\)

\(\hbox {u}_{x4}\)

11

\(\hbox {u}_{y4}\)

4.\(8 \times 10^{-1}\)

\(\hbox {u}_{y1}\)

76

\(\hbox {u}_{y1}\)

18

\(\hbox {u}_{x1}\)

9.5

\(\hbox {u}_{x1}\)

87

\(\hbox {u}_{x2}\)

21

\(\hbox {u}_{y1}\)

10

\(\hbox {u}_{y2}\)

93

\(\hbox {u}_{x1}\)

25

\(\hbox {u}_{x4}\)

18

\(\hbox {u}_{x2}\)

95

\(\hbox {u}_{y2}\)

51

\(\hbox {u}_{y2}\)

29

\(\hbox {u}_{z1}\)

100

\(\hbox {u}_{z1}\)

100

\(\hbox {u}_{z1}\)

100