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Table 4 BTD models for 0/90/0, \(\hbox {R/a} = 5\), \(\hbox {a/h} = 5\)

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

DOF

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

15

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

14

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

13

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

12

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

11

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

10

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

9

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

8

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

7

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

6

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\blacktriangle \)

5

\(\blacktriangle \)

\(\blacktriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\blacktriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

\(\vartriangle \)

Ā 

\(\hbox {RF}_0 = 1.00\)

\(\hbox {RF}_1 = 0.73\)

\(\hbox {RF}_2 = 0.45\)

\(\hbox {RF}_3 = 0.76\)

\(\hbox {RF}_4 = 0.39\)