# Static and Dynamic Response of FG-CNT-Reinforced Rhombic Laminates
## 5 Numerical Results and Discussion
### Results and Discussion
#### 5.2.2 Static Analysis  
The dimensionless maximum deflection of a FG-CNT-reinforced rhombic plate under uniform loading for simply supported and clamped boundary conditions is shown in Tables 14 and 15, respectively. The volume fraction of CNT was taken as 0.11, 0.14 and 0.17. The results were tabulated for UD and FG-CNT-reinforced rhombic plate with \(a/b=1\) and \(a/h=10\). It can be observed that an increase in the volume fraction of CNTs results in a decrease in the deflection of CNTRC rhombic plate because of the fact that the higher value of volume fraction has higher stiffness; thus, the deflection is reduced. It is anticipated that there is a nearly 36% decrease shown in maximum deflection for both clamped and simply supported boundary conditions as the value of \(V^{*}_{\mathrm{CNT}}\) increases from 0.11 to 0.17 and approximately 6% decreases are noticed when \(V^{*}_{\mathrm{CNT}}\) changes from 0.11 to 0.14. Maximum dimensionless deflection decreases with an increase in the skew angle because it reduces the length of the shorter diagonal leading to an enhancement in the stiffness of the rhombic plate. Thus, the deflection is reduced. Figure 3: Variation of non-dimensional frequency parameter of FG-CNT-reinforced rhombic plate with aspect ratio; (**A**) \(\alpha=15^{\circ}\) and (**B**) \(\alpha=30^{\circ}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Types**} & \multirow{2}{*}{\(\boldsymbol{V^{*}_{\text{CNT}}}\)} & \multicolumn{4}{c}{**Skew Angle**} \\ \cline{3-6}  & & \(\boldsymbol{15^{\circ}}\) & \(\boldsymbol{30^{\circ}}\) & \(\boldsymbol{45^{\circ}}\) & \  
Tables 16 and 17 represent the dimensionless maximum deflection of simply supported and clamped FG-CNT-reinforced rhombic plate under sin-sin loading, respectively. Here, an approximately 25% decrease in the maximum dimensionless deflection is noticed when the skew angle changes from 15\({}^{\circ}\) to 30\({}^{\circ}\); 40% decreases when the skew angle changes from 30\({}^{\circ}\) to 45\({}^{\circ}\) and 55% decreases when the skew angle changes from 45\({}^{\circ}\) to 60\({}^{\circ}\) for both uniform loading and sin-sin loading. The lowest and highest dimensionless deflection was found for FG-O- and FG-X-type CNT distribution, respectively. Figure 5 shows the variation of dimensionless deflection of FG-V CNT-reinforced rhombic plate along the length (x/_a_) at y/_b_ = 0.50 for four skew angles under sin-sin loading. It can be seen that all values of CNT volume fraction have the same nature of deflection along the length and for the skew angle 60\({}^{\circ}\), negative deflection is noticed for the farther end subjected to sin-sin loading. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Types**} & \multirow{2}{*}{\(\mathbf{V^{*}}_{\text{CNT}}\)} & \multicolumn{4}{c}{**Skew Angle**} \\ \cline{3-6}  & & **15\({}^{\circ}\)** & **30\({}^{\circ}\)** & **45\({}^{\circ}\)** & **60\({}^{\circ}\)** \\ \hline UD & 0.11 & 0.00215 & 0.00158 & 0.00092 & 0.00038 \\  & 0. The effect of loading type on the non-dimensional deflection of simply supported and clamped FG-V type CNT-reinforced rhombic plate with skew angle was shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Types**} & \multirow{2}{*}{\(\boldsymbol{V^{*}}_{\text{CNT}}\)} & \multicolumn{4}{c}{**Skew Angle**} \\ \cline{3-6}  & & \(\boldsymbol{15^{\circ}}\) & \(\boldsymbol{30^{\circ}}\) & \(\boldsymbol{45^{\circ}}\) & \(\boldsymbol{60^{\circ}}\) \\ \hline UD & 0.11  
The non-dimensional maximum deflection decreased with an increase in the skew angle for uniform and sin-sin loading, while under the cos-cos loading, the value of \(\overline{w}\) increases first and then decreases as the skew angle grows.