Modeling of cylindrical composite shell structures based on the Reissner’s Mixed Variational Theorem with a variable separation method

Table 7 Three layers \([45^{\circ }/-45^{\circ }/45^{\circ }]\,\)– \(\phi =1\)—S = 4

\({{\varvec{z/e}}}\)	\(\bar{{{\varvec{u}}}}\)		\(\bar{{{\varvec{w}}}} \)		\(\bar{\varvec{\sigma }}_{{{\varvec{11}}}}\)		\(\bar{\varvec{\sigma }}_{{{\varvec{13}}}}\)		\(\bar{\varvec{\sigma }}_{{{\varvec{33}}}}\)
\({{\varvec{z/e}}}\)	VS-LM4	exact	VS-LM4	Exact	VS-LM4	Exact	VS-LM4	Exact	VS-LM4	Exact
\(-\) 1/2	\(-\) 2.41	\(-\) 2.42	7.297		\(-\) 1.16	\(-\) 1.16	0.00	0	0.00	0
\(-\) 1/3	\(-\) 2.14	\(-\) 2.14	7.329		\(-\) 0.43	\(-\) 0.43	0.42	0.42	\(-\) 0.41	\(-\) 0.41
\(-\) 1/6\(^{-}\,\)	\(-\) 1.68	\(-\) 1.69	7.329		0.05	0.05	0.48	0.48	\(-\) 0.26	\(-\) 0.26
\(-\) 1/6\(^+\)	\(-\) 1.68	\(-\) 1.69	7.329		\(-\) 0.61	\(-\) 0.61	0.48	0.48	\(-\) 0.26	\(-\) 0.26
0	\(-\) 0.02	\(-\) 0.02	7.320	7.319	\(-\) 0.02	\(-\) 0.02	0.59	0.60	\(-\) 0.15	\(-\) 0.15
1/6\(^{-}\,\)	1.51	1.51	7.318		0.51	0.51	0.43	0.43	0.27	0.27
1/6\(^+\)	1.51	1.51	7.318		\(-\) 0.04	\(-\) 0.04	0.43	0.43	0.27	0.27
1/3	1.84	1.84	7.325		0.39	0.39	0.32	0.32	0.56	0.56
1/2	2.03	2.02	7.334		0.92	0.92	0.00	0	1.00	1.