Research Article

Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method

Table 1

First ten frequencies and maximum static deflections for the six shell structures of Figure 4 made of isotropic materials: : full ceramic material and : full metal material using a Chebyshev-Gauss-Lobatto (C-G-L) grid distribution with different boundary conditions.

Square plate CCFFCylindrical panel SFSFConical shell CFToroidal shell panel CFCatenoidal panel CFCFElliptic paraboloid CCCC
Mode [Hz]
GDQ ( )GDQ ( )GDQ ( )GDQ ( )GDQ ( )GDQ ( )GDQ ( )GDQ ( )GDQ ( )GDQ ( )GDQ ( )GDQ ( )

375.598162.089271.645115.701449.402194.32328.66512.452828.011359.407451.863201.635
1252.975536.895282.473120.922449.402194.32329.38512.679846.255365.918485.074211.268
1373.081602.852546.801234.445585.799247.96580.33034.3971042.714451.381487.409212.299
2367.2391019.777549.102239.032585.799247.96580.41634.7061136.811486.278632.857276.825
2868.5971235.869642.802276.494680.296298.116113.94849.1151147.395492.825719.612314.418
3084.9921334.067648.822279.014680.296298.116121.53352.6841212.360518.534747.215328.314
3194.3521399.648847.611371.648860.268373.956133.55357.4521476.266632.458864.072377.506
3629.6671590.719933.540404.836860.268373.956160.57570.0621566.446679.318878.506383.706
4018.9361736.048973.695423.554930.739411.564167.11571.9791890.222821.6201019.096443.351
4156.4831800.8731143.969483.642966.531418.914197.56685.1081941.698833.1591034.972450.206