Table 5: Clamping options for +45/−45/+45/−45 hypar shells with central cutouts having a′/a ratio 0.2.

Number of sides to be clampedclamped edgesImprovement of frequencies with respect to simply supported shellsMarks indicating the efficiencies of clamping

0Simply supported no edges clamped (SSSS)0
1(a) Along (CSSS)Slight improvement9
(b) along (SSCS)Slight improvement9
(c) along (SSSC)Slight improvement10
2(a) Two alternate edges (CSCS, SCSC)Good improvement22
(b) Two adjacent edges (CSSC, CCSS)Marked improvement52
33 edges excluding CSCCRemarkable improvement72
3 edges excluding CCSCRemarkable improvement72
3 edges excluding CCCSRemarkable improvement72
4All sides (CCCC)Frequency attains a maximum value100