*4.4. Influence of* 0◦*-Ply Ratio on the Effective Performance of OSFP*

The 0◦ ply ratio *r* was the ratio of the number of 0◦-ply to the total number of ply. To study the influence of 0◦-ply ratio on the effective performance of the panel, the 10 layered laminate with combination of 0◦ and 45◦ plies was considered, and the six layup configurations are illustrated in Figure 15.

**Figure 15.** Six different 0◦-ply ratios in the layup combination of 0◦ and 45◦ plies.

Figure 16a shows that the influences of the 0◦-ply ratio on *A*<sup>11</sup> and *D*<sup>11</sup> were much greater than those on the other stiffness components because the stiffness along the fiber direction (0◦ direction) was stronger. Figure 16b shows that the first natural frequency increased with increasing 0◦-ply ratio and reached a maximum value when the 0◦ ply ratio was 100%. The third to fourth natural frequencies increased first and then decreased and reached the maximum value when the 0◦-ply ratio was between 0.2 and 0.6. With the increase in the 0◦-ply ratio, the first to fourth buckling loads of the OSFP increased gradually and reached a maximum value when the 0◦ ply ratio was 100%. In engineering applications, the effective performance of the OSFP in the corresponding direction can be improved by adjusting the 0◦-ply ratio.

(**a**) Equivalent stiffness

(**b**) Natural frequency and buckling load

**Figure 16.** Effects of the structural parameters on the effective performances of the OSFP.

#### **5. Comparison with Other Stiffened FRP Panels with Different Stiffening Forms**

To compare the effects of different stiffening forms on the effective performance of the OSFP, the 3D FE models and 2D reduced-order plate models of orthogrid-, T-, and blade-stiffened FRP panel were established. The 3D FE models were obtained by repeating the unit cell 15 times in the *x*<sup>1</sup> and *x*<sup>2</sup> directions as shown in Figure 17. The structural parameters of unit cell were *l* = 20 mm, *h* = 3 mm, and *t* = 1 mm. The material parameters were the same as in Section 4, and the layup configurations of skin and stiffener were [45/ − 45/0/ − 45/45]2*<sup>s</sup>* and [45/ − 45]4*s*, respectively.

**Figure 17.** 3D finite element model and its unit cell of stiffened FRP panels with different stiffening forms.

The static displacements along the center line of the stiffened FRP panels under the CCCC boundary condition and 5 kPa of uniform load were analyzed. The comparative results in Figure 18 show that the displacement of the blade-stiffened FRP panel was the largest, followed by the orthogrid- and T-stiffened FRP panels due to the fact that the equivalent bending stiffness of T-stiffened FRP panel was greater than the other two stiffened FRP panels.

**Figure 18.** Comparison of the displacements along the center line of the stiffened FRP panel with different stiffening forms under the CCCC boundary condition and a 5 kPa uniform load.

Table 4 shows the first four natural frequencies of the stiffened FRP panel with different stiffening forms under the CCCC boundary condition. The first natural frequency of the T-stiffened FRP panel was the largest. From the second order, the natural frequency of the orthogrid-stiffened FRP panel was the largest, followed by the T- and blade-stiffened FRP panels.

**Table 4.** Influence of the different stiffening forms on the natural frequencies (Hz) of stiffened FRP panels under the CCCC boundary condition.

The comparative results showed that the natural frequencies of the OSFP increased faster with increasing modal order, while those of the T- and blade-stiffened FRP panels showed little change. The vibration modes of the T- and blade-stiffened FRP panels were basically the same, but the vibration modes of the orthogrid-stiffened FRP panel were very different (there were one and two half-waves along the *x*<sup>1</sup> direction, two half-waves along the *x*<sup>2</sup> direction, and two half-waves along the *x*1, and *x*<sup>2</sup> directions for the first, second, third, and forth mode shapes, respectively). It was concluded that the vibration modes of the stiffened FRP panel could be changed by adjusting the stiffening forms.
