*4.1. Influence of Structural Parameters on Equivalent Plate Properties*

Figure 12a shows the effect of the stiffener thickness on the equivalent stiffness of the OSFP when the other parameters remained unchanged. The equivalent stiffness *Aij* and *Dij* increased with increasing stiffener thickness, and in particular, the bending stiffness components *D*<sup>11</sup> and *D*<sup>22</sup> increased significantly. This may be because *Aij* was directly proportional to the cross-sectional area, which increased with increasing stiffener thickness. In contrast, *Dij* was proportional to the moment of inertia, which was linearly related to the stiffener thickness.

Figure 12b shows the effect of stiffener height on the equivalent stiffness when other parameters remain unchanged. It can be seen that *Aij* increased linearly and *Dij* increased nonlinearly with the increasing stiffener height. The reason was that *Aij* was proportional to the sectional area, which was linear with the stiffener height, while *Dij* was proportional to the moment of inertia, resulting in a parabolic growth trend.

Figure 12c shows the effect of length–width ratio on the equivalent stiffness. It can be observed that *A*<sup>11</sup> and *D*<sup>11</sup> had no obvious change with the increasing length–width ratio, while *D*<sup>22</sup> decreased significantly. The reason was that the extension area and moment of inertia in *x*<sup>1</sup> direction remained unchanged, while the extension area and moment of inertia in the *x*<sup>2</sup> direction gradually decreased with the increasing length–width ratio, which led to the nonlinear decrease in equivalent bending stiffness.

Figure 12d shows the effect of the periodic length on the equivalent stiffness of the stiffened FRP panel. It can be observed that *Aij* and *Dij* decreased nonlinearly with the increase in periodic length. This was because *Aij* and *Dij* were, respectively, proportional to the extension area and the moment inertia, and there was a negative nonlinear relationship between the extension area/moment inertia and the periodic length, resulting in a parabolic downward trend with the increasing periodic length.

**Figure 12.** Effects of the structural parameters on the equivalent plate properties of the OSFP.

#### *4.2. Influence of Structural Parameters on Buckling Loads and Natural Frequencies*

To further investigate the influence of structural parameters on the effective performance of OSFP, the first four buckling loads and natural frequencies of OSFP with different stiffener height, thickness, periodic length, and length–width ratio were calculated by using 2D-RPM, as shown in Figure 13.

The first four natural frequencies of the OSFP increased with increasing stiffener thickness and height and decreased with increasing length–width ratio and periodic length. The effect of the stiffener height *h* on the natural frequency was much greater than that of other structural parameters. The reason is that the variation trends of the equivalent stiffness and equivalent mass were consistent with those of structural parameters, and their influences on the natural frequency might counteract each other. However, the effect of the stiffener height *h* on the equivalent stiffness was much greater than that on the equivalent mass. The buckling load of the OSFP increased with the increase in stiffener thickness and height but decreased with increasing length–width ratio and periodic length, which was the same as the change trend of equivalent stiffness.

**Figure 13.** Effects of the structural parameters on the natural frequency and buckling load of the OSFP.

#### *4.3. Influence of Layup Configuration on the Effective Performance of OSFP*

The layup configurations of the laminates would affect the effective performance of the OSFP due to the anisotropy and heterogeneity. In this section, the influences of the layup configuration on the equivalent stiffness, free vibrations, and buckling mode of the OSFP are analyzed. The layup configuration was set to [0/*θ*/0/*θ*/0]s, where *θ* increased from 0◦ to 90◦ at 15◦ intervals. The boundary condition was fixed on one side and simply supported on three sides (CSSS).

Figure 14a shows the effect of the layup configuration on the equivalent stiffness of the OSFP. With the gradual increase in the ply angle, the stiffness components *A*<sup>11</sup> and *D*<sup>11</sup> showed nonlinear downward trends, while *A*<sup>22</sup> and *D*<sup>22</sup> showed significant nonlinear increases when the ply angle was greater than 45◦. Figure 14b shows the effect of the layup configuration on the first four natural frequencies and buckling loads of the OSFP. It can be observed that the layup configuration had little effect on the natural frequency, and the first natural frequency first decreased and then increased with the increasing ply angle, reaching the minimum value in the range of 30–60◦ ply angle. The buckling load first increased and then decreased with the increasing ply angle, and the buckling load of each order reached the maximum value at 30–45◦ ply angle.

**Figure 14.** Effects of the layup configuration on the effective performances of the OSFP.
