Table 2 Displacement and energy evaluation of the three-layered cylindrical panel under bending, obtained through hierarchical elements with \(p=7\)
\({{\varvec{R}}}_{\varvec{\beta }}{{\varvec{/h}}}\) | TOS | Integration | \(\bar{{\varvec{w}}}\) (%)– | \({\varvec{E}}_{{\varvec{memb}}}/{\varvec{E}}\) (%) | \({\varvec{E}}_{{\varvec{bend}}}/{\varvec{E}}\) (%) | \({\varvec{E}}_{{\varvec{ps}}}/{\varvec{E}}\) (%) | \({\varvec{E}}_{{\varvec{zs}}}/{\varvec{E}}\) (%) | \({\varvec{E}}_{{\varvec{zz}}}/{\varvec{E}}\) (%) |
|---|---|---|---|---|---|---|---|---|
10 | FSDT | FULL | 294.5 | 0.0 | 20.5 | 0.0 | 79.5 | – |
LE4 | FULL | 330.4 | 0.0 | 17.0 | 0.0 | 59.5 | 23.5 | |
LE4 | REDI | 329.9 | 0.0 | 17.0 | 0.0 | 59.4 | 23.6 | |
LE4 | SELI | 330.4 | 0.0 | 17.0 | 0.0 | 59.5 | 23.5 | |
100 | FSDT | FULL | 61.67 | 0.0 | 96.3 | 0.0 | 3.7 | – |
LE4 | FULL | 62.45 | 0.0 | 95.0 | 0.0 | 5.0 | 0.0 | |
LE4 | REDI | 62.33 | 0.0 | 95.0 | 0.0 | 5.0 | 0.0 | |
LE4 | SELI | 62.45 | 0.0 | 95.0 | 0.0 | 5.0 | 0.0 | |
1000 | FSDT | FULL | 59.57 | 0.0 | 100.0 | 0.0 | 0.0 | – |
LE4 | FULL | 59.58 | 0.0 | 99.9 | 0.0 | 0.1 | 0.0 | |
LE4 | REDI | 59.48 | 0.0 | 99.9 | 0.0 | 0.1 | 0.0 | |
LE4 | SELI | 59.58 | 0.0 | 99.9 | 0.0 | 0.1 | 0.0 | |
5000 | FSDT | FULL | 59.61 | 0.0 | 100.0 | 0.0 | 0.0 | – |
LE4 | FULL | 59.61 | 0.0 | 100.0 | 0.0 | 0.0 | 0.0 | |
LE4 | REDI | 59.52 | 0.0 | 100.0 | 0.0 | 0.0 | 0.0 | |
LE4 | SELI | 59.61 | 0.0 | 100.0 | 0.0 | 0.0 | 0.0 |