# Static and Dynamic Response of FG-CNT-Reinforced Rhombic Laminates
## 5 Numerical Results and Discussion
### Convergence and Validation of Present Formulation
#### 5.1.2. Bending Analysis  
**Example 4.** Table 7 depicts the convergence study for dimensionless maximum deflection for UD and FG-CNT-reinforced functionally graded rhombic plate. The dimensionless maximum deflection of the UD, FG-V, FG-O and FG-X CNTRC rhombic plate was computed for different mesh size and clamped boundary condition. The results were computed for \(V^{\bullet}_{\textbf{CNT}}\) = 0.11. The convergence study showed that 16 \(\times\) 16 mesh size is acceptable for the present model using the discussed nine-noded isoparametric elements. Hence, 16 \(\times\) 16 mesh size was chosen for all the parametric studies of the bending analysis of functionally graded CNTRC rhombic plate.  
**Example 5.** The dimensionless central deflection (_w/h_) of the uniformly distributed CNT-reinforced composite plate with different side-to-thickness ratios and end supports were presented in Tables 8 and 9. The non-dimensional central deflection was compared with [PERSON] et al. [5]; \(V^{\bullet}_{\textbf{CNT}}\) = 0.11, 0.14 and _a/h_ = 10, 20, 50 were used for the comparison study. The dimensionless central deflection of different types of boundary condition was found to be in decent agreement with [PERSON] et al. [5].  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**BC**} & \multirow{2}{*}{\(V^{\bullet}_{\textbf{CNT}}\)} & \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{_a/h = 10_} & \multicolumn{2}{c}{_a/h = 20_} & \multicolumn{2}{c}{_a/h = 50_} \\ \cline{3-8}  & & & **[PERSON] et al. [5]** & **Present** & **[PERSON] et al. [5]** & **Present** & **[PERSON] et al. [5]** & **Present** \\ \hline CCCC & 0.11 & 1 & 17.211 & 17.753 & 26.304 & 26.693 & 34.165 & 34.480 \\  & & 2 & 22.812 & 23.462 & 31.496 & 32.099 & 39.043 & 39.584 \\  & & 3 & 33.070 & 34.035 & 43.589 & 44.133 & 51.204 & 51.815 \\  & & 4 & 33.552 & 34.355 & 56.249 & 57.061 & 72.202 & 71.954 \\  & & 5 & 36.528 & 37.889 & 59.249 & 60.253 & 86.291 & 86.133 \\  & & 6 & 37.437 & 38.841 & 62.608 & 62.218 & 89.054 & 89.105 \\  & 0.14 & 1 & 17.791 & 18.405 & 27.926 & 28.371 & 37.568 & 37.909 \\  & & 2 & 23.413 & 24.113 & 32.976 & 33.629 & 42.175 & 42.733 \\  & & 3 & 34.101 & 34.792 & 44.989 & 45.573 & 53.963 & 54.590 \\  & & 4 & 34.275 & 35.553 & 58.951 & 59.968 & 74.785 & 74.546 \\  & & 5 & 37.538 & 39.053 & 61.816 & 63.051 & 94.022 & 93.911 \\  & & 6 & 38.159 & 39.574 & 64.135 & 63.758 & 96.573 & 96.680 \\ \hline SSSS & 0.11 & 1 & 12.452 & 12.601 & 15.110 & 15.291 & 16.252 & 16.465 \\  & & 2 & 17.060 & 17.409 & 19.903 & 20.297 & 21.142 & 21.573 \\  & & 3 & 19.499 & 19.479 & 31.561 & 32.106 & 33.350 & 33.993 \\  & & 4 & 19.499 & 19.484 & 38.998 & 38.959 & 53.430 & 53.670 \\  & & 5 & 27.340 & 27.762 & 38.998 & 38.969 & 60.188 & 60.337 \\  & & 6 & 31.417 & 31.903 & 47.739 & 47.899 & 62.198 & 63.042 \\  & & 1 & 13.256 & 13.415 & 16.510 & 16.701 & 17.995 & 18.228 \\  & & 2 & 17.734 & 18.090 & 21.087 & 21.483 & 22.643 & 23.082 \\  & & 3 & 19.879 & 19.871 & 32.617 & 33.163 & 34.660 & 35.306 \\  & & 4 & 19.879 & 19.876 & 39.759 & 39.742 & 54.833 & 55.062 \\  & & 5 & 28.021 & 28.449 & 39.759 & 39.752 & 66.552 & 66.712 \\  & & 6 & 32.678 & 33.284 & 51.078 & 51.122 & 68.940 & 69.212 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison study of first six non-dimensional frequency parameter of FG-V CNT-reinforced composite plate.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mesh** & **UD** & **FG-V** & **FG-O** & **FG-X** \\ \hline
8 \(\times\) 8 & 0.00372 & 0.00422 & 0.00588 & 0.00309 \\
10 \(\times\) 10 & 0.00361 & 0.00411 & 0.00576 & 0.00297 \\
12 \(\times\) 12 & 0.00355 & 0.00406 & 0.00568 & 0.00292 \\
14 \(\times\) 14 & 0.00349 & 0.00402 & 0.00561 & 0.00289 \\
16 \(\times\) 16 & 0.00345 & 0.00401 & 0.00557 & 0.00287 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Convergence of non-dimensional maximum deflection of CNT-reinforced functionally graded clamped rhombic plate.