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

Advanced Modeling and Simulation in Engineering Sciences

Table 1 Convergence study—one layer \([0^{\circ }]\)—S = 40—\(\phi =\pi /3\)— \(N_z = NC\)—mesh \(N_x \times 10\) with space ratio (50)

\({{\varvec{N}}}_{{\varvec{x}}}\)		\({\bar{{\varvec{u}}}}{{\varvec{(0,e/2)}}}\)	\(\bar{{{\varvec{w}}}}{{\varvec{(L,0)}}}\)	\(\bar{\varvec{\sigma }}_{{{\varvec{11}}}}{{\varvec{(-e/2)}}}\)	\(\bar{\varvec{\sigma }}_{{{\varvec{13}}}}{{\varvec{(0)}}}\)	\(\bar{\varvec{\sigma }}_{{{\varvec{33}}}}\) max
4	VS-LM4	9.3287	0.0779	\(-\) 0.8406	0.3181	\(-\) 8.7001
4	Error	0.51%	0.02%	8.79%	44.08%	22.50%
8	VS-LM4	9.3744	0.0780	\(-\) 0.7908	0.5061	\(-\) 7.5489
8	Error	0.02%	0.10%	2.35%	11.02%	6.29%
14	VS-LM4	9.3769	0.0780	\(-\) 0.7786	0.5484	\(-\) 7.2645
14	Error	0.00%	0.04%	0.77%	3.60%	2.29%
20	VS-LM4	9.3775	0.0780	\(-\) 0.7756	0.5590	\(-\) 7.1931
20	Error	0.01%	0.03%	0.38%	1.73%	1.28%
26	VS-LM4	9.3775	0.0780	\(-\) 0.7744	0.5633	\(-\) 7.1654
26	Error	0.01%	0.02%	0.22%	0.97%	0.89%
32	VS-LM4	9.3775	0.0780	\(-\) 0.7738	0.5651	\(-\) 7.1503
32	Error	0.01%	0.02%	0.14%	0.67%	0.68%
	Navier	9.3778	0.0780	\(-\) 0.7727	0.5688	\(-\) 7.1074
	Exact	9.3765	0.0780	\(-\) 0.7727	0.5688	\(-\) 7.1021