1. UB LB UB LB UB LB 1 - 26.67 34.29 26.67 - 2 - 8.89 - 8.89 - 3 - b 5b b - 0.3b 4 - 0. 5b - 0.5b - 0.3b 5 - 0.3b - 0.3b - 0.3b 6 - 0.3b - 0.3b - 0.3b 7 - b 9b b - 0.3b 8 - 0.3b - 0.3b - 0.3b 9 - 0.3b 2b 0.3b - 0.3b
2. This example illustrates the use of the VICON type analysis feature in VICONOPT. The panel of Example l was restrained by point supports applied at x=O to the g nodes of Fig. 4(b) which restrained displacement in the x and z directions. This point support positioning does not form a particularly likely set but was chosen because VICONOPT does not permit constraints within substructures and because it was decided to retain the model of Fig. 4(b), since it was used for Examples 1-3. Such point supports could be considered to represent a particular form of transverse line support to low accuracy. However, to obtain higher accuracy and a more realistic form of line support it would be necessary to use point supports in the way described in connection with Table 1 of the companion paper 3 This panel was loaded in axial compression by a total load of 1921.63 kN. A shear load per unit width of 788.070 kN/m was applied to the plates which represent the skin and the skin plus the stiffener upper flange. The latter was modelled as one asymmetric plate with offsets to avoid the shear distribution which would be necessary if, as in Examples l - 3, it were modelled as two symmetric plates. The initial breadths of plates in the skin were increased from the 12.70 mm and 10.16 mm of Example l to 50.80 mm and 25.40 mm respectively and the stiffener upper flange breadths were increased from the 10.16 mm of Example 1 to 25.40 mm. Figure 4(a) shows these plate breadths as broken lines. Table 2 gives the new bounds on design variables which were used for this example, which consist only of lower bounds on the plate thicknesses. VIPASA type analysis was used for the short wavelength modes, by using A= e/i for i=3,4,5,30. VICON type analysis was used to cover the overall modes by coupling from 2 to 5 of the longer wave-7engths (i.e. see the companion pape r3with its q=2) in a way which was compatible with the transverse supports. The VICON analysis was carried out for values of - of O, 0 . 2 5 , 0 . 5 , 0 . 75 and l . 0 . VI CON analysis was necessary for this problem to maintain compatibility with transverse supports that restrained the overall shear mode which would otherwise be skewed. Such restraint increases the load carrying capacity of the panel with respect to these overall modes, an increase which is ignored by VIPASA analysis and only approximated for in PASCO. The initial configuration of this example does not carry the design load. The critical VIPASA short wavelength mode is at A= e/3 whilst the critical VICON overall mode occurs with-= 0.75. The buckling load factors for these two modes are 0.856 and 0.576 respectively. VICONOPT achieves a 14% mass reduction from the initial configuration after stabilization in 7 sizing cycles involving 3, 3, 2 , 3, 3, 2 and 2 CONMIN cycles respectively. The final configuration carries the load with a critical overall buckling load factor of 1.00, with-= 0.75, and a critical local buckling load factor with= 2/3 of 1.37. Table 3 gives a breakdown of the VICONOPT CPU timing for this problem. A more accurate VICON analysis which coupled up to wavelengths (i.e. see the companion paper with its q=5) gave a buckling load factor of 0.930 at-= 0.75 for this final configuration. Stabilization to this higher VICON accuracy resulted in an increased mass of 3% relative to the final design to lower VICON accuracy. This stabilization was initiated manually but could be added to VICONOPT as an automated feature to avoid unsafe errors. Compared with doing this,results for a similar problem using the larger number of wavelengths throughout took over twice as much computer time and achieved the same minimum mass.
3. Buckling and vibration of any prismatic assembly of shear and compression loaded anisotropic plates with an arbitrary supporting structure