## 9 Numerical Results and Discussion
### Bending
Additionally, if the volume fraction coefficient was fixed, then if the slenderness ration increased, the dimensionless displacement decreased. Table 6 presents the dimensionless maximum deflection for various values of the nonlocal parameter ea, material length parameter \(l\), and slenderness ratio _L/h_ for the Euler-Bernoulli beam and Timoshenko CNTRC nanobeam. Table 7 presents the errors and percentages comparing results known in literature and results obtained in this work, \(error=|R_{k}-R_{p}|\); \(p=\frac{error}{R_{k}}100\), where \(R_{k}\) represents results known in literature. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{_L/h = 10_} & \multicolumn{3}{c}{_L/h = 20_} & \multicolumn{3}{c}{_L/h = 50_} \\ _ea_ & **Beam** & \multicolumn{3}{c}{_L = 0 nm_} & \multicolumn{3}{c}{_l = 2 nm_} & \multicolumn{3}{c}{_l = 0 nm_} & \multicolumn{3}{c}{_l = 2 nm_} & \multicolumn{3}{c}{_l = 0 nm_} & \multicolumn{3}{c}{_l = 2 nm_} \\ _nem_ & **Theory** & **Data** & **Data** & **Present** & **from** & **Present** & **from** & **Present** & **from** & **Present** & **from** & **Present** & **from** & **Present** \\  & & **[6]** & & **[6]** & & **[6]** & & **[6]** & & **[6]** & & & **[6]** & \\ \hline \multirow{2}{*}{0} & E-B & 1.3021 & 1.3057 & 0.9360 & 0.9401 & 1.3021 & 1.3091 & 1.1840 & 1.1797 & 1.3021 & 1.3092 & 1.2823 & 1.2857 \\  & T & 1.3346 & 1.3407 & 0.9598 & 0.9587 & 1.3102 & 1.3142 & 1.1944 & 1.1896 & 1.3034 & 1.3104 & 1.2836 & 1.2873 \\ \hline \multirow{2}{*}{1} & E-B & 1.4271 & 1.4283 & 0.9596 & 0.9588 & 1.3333 & 1.3412 & 1.2157 & 1.2095 & 1.3071 & 1.3106 & 1.2873 & 1.2904 \\  & T & 1.4622 & 1.4803 & 1.0275 & 1.1029 & 1.3416 & 1.3391 & 1.2234 & 1.2303 & 1.3084 & 1.3109 & 1.2986 & 1.0907 \\ \hline \multirow{2}{*}{2} & E-B & 1.8021 & 1.8095 & 1.3021 & 1.3076 & 1.4271 & 1.4266 & 1.3021 & 1.3077 & 1.3221 & 1.3276 & 1.3021 & 1.3071 \\  & T & 1.8450 & 1.8507 & 1.3346 & 1.3391 & 1.4359 & 1.4388 & 1.3102 & 1.3114 & 1.3234 & 1.3255 & 1.3034 & 1.3085 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of dimensionless maximum deflection for CNTR, Euler–Bernoulli beam, and Timoshenko beam for different values of ea, \(l\), and _L/h_. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(V_{CNT}\)} & \multicolumn{3}{c}{**Maximum Normalized Deflection: 10\(w\)**} \\ \cline{2-5}  & **Data from [10]** & **Present** \\ \hline
0.12 & 0.515866 & 0.512437 \\
0.17 & 0.323635 & 0.324072 \\
0.28 & 0.242150 & 0.243075 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The maximum normalized buckling loads for different values of the volume fraction parameter. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(V_{CNT}\)} & \multirow{2}{*}{_L/h_} & \multicolumn{3}{c}{**Dimensionless Displacement**} \\ \cline{3-5}  & & **Data from [3]** & **Present** \\ \hline  & & 10 & 0.704 & 0.695 \\
0.12 & 15 & 0.524 & 0.518 \\  & 20 & 0.461 & 0.458 \\ \hline  & & 10 & 0.448 & 0.439 \\
0.17 & 15 & 0.344 & 0.351 \\  & 20 & 0.307 & 0.310 \\ \hline  & & 10 & 0.325 & 0.328 \\
0.28 & 15 & 0.235 & 0.241 \\  & 20 & 0.203 & 0.205 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Dimensionless displacements without NSGT for uniform beam. From Table 7, we can conclude that the results obtained in the present work for different cases were in very good agreement with the results obtained in literature. Additionally, from Tables 1-3, it is clear that the results obtained using our procedure for the nonlinear cases were substantially different when comparing the results with those obtained for linear cases. We observed that the dimensionless maximum deflection of the Euler-Bernoulli beam was lower in comparison with the Timoshenko beam. Additionally, it can be seen that if _ea_ increased, then dimensionless maximum deflection decreased, and if \(l\) increased and _ea_ was unchanged, then the dimensionless maximum deflection decreased.