## 9 Results and Discussion
The critical buckling load is increased with the increasing of number of stiffeners, while the critical buckling load has a greater value at (S-C-S-C) boundary conditions. The ANSYS program is used in the calculation of the critical buckling load. Figure 30 shows the critical buckling load against the stiffener-depth ratio for (S-S-S-S) boundary conditions in the presence of the in-plane compression mechanical load and shear force for the plate with one and two stiffeners. The buckling load is varied sinusoidal with the increasing stiffener-depth ratio. As mentioned, the critical buckling load is increased  
Figure 28: Critical buckling load against lamination angle for (S-C-S-C) and (S-F-S-F) boundary conditions. Figure 29: Critical buckling load against number of stiffeners at (S-F-S-F, S-S-S-S and S-C-S-C) boundary conditions. with the increasing of number of stiffeners. The ANSYS program is used in the calculation of the critical buckling load. Figure 31 shows the buckling factor against the aspect ratio of (S-S-S-S) boundary conditions for the plate with one stiffener in the presence of in-plane compression mechanical load and shear force. The buckling factor of the buckling mode is decreased with the increasing aspect ratio until it settles down at buckling factor (20). The analytical results of the critical buckling load of the buckling mode have been completed using the Navier solution of classical laminate plate theory. Figure 32 shows the buckling factor against the aspect ratio for the plate with two stiffeners of (S-S-S) boundary conditions. Figure 31: Buckling factor against aspect ratio for (S-S-S-S) simply supported boundary conditions for plate with one stiffener. Figure 30: Critical buckling load against stiffener–depth ratio for (S-S-S-S) boundary conditions. Table 2 shows the comparison of the critical buckling load when the composite laminated plate is supported with one and two stiffeners at different boundary conditions. The value of the critical buckling load is increased with the increasing of number of stiffeners for different boundary conditions. The numerical results of the critical buckling load were calculated using the ANSYS program, while the analytic results were calculated using the Levy solution of (S-C-S-C, S-C-S-S, S-F-S-C, S-F-S-S and S-F-S-F) boundary conditions. The analytic results of the (S-S-S-S) boundary condition were determined using the Navier solution of classical laminate plate theory. Figures 33-35 show the largest Lyapunov exponent against aspect ratios for the un-stiffened plate and plate with one and two stiffeners at different fiber volume fractions. As mentioned, that Lyapunov exponent is the indicator to the non-periodic motion and chaos (nonlinear dynamic phenomena) for the bending deflection of stiffened and un-stiffened composite laminated plate. The nonlinear dynamic behavior of the bending deflection is increased with the increasing of the aspect ratios and fiber volume fractions. All the values of the largest Lyapunov exponent are positive and above zero, which means that the motion of the bending deflection is non-periodic. The nonlinear dynamic phenomena are decreased with the use of beam stiffeners. The system with aspect ratio (2.5) and fiber volume fraction (\(\
u_{\text{f}}=80\%\)) for the un-stiffened plate is more chaotic than the other systems, as indicated in Figure 33. The nonlinear dynamic phenomena is very low for the system with aspect ratio (2.5) and fiber volume fraction (\(\
u_{\text{f}}=80\%\)) after using plate with two stiffeners, as shown in Figure 22:0 The ANSYS program is used in the calculation of bending deflection.