# Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment
## 5 Results and Discussion
### Parametric Study  
The parametric study in this section assumes a PmPV as core material and as matrix phase for the face sheets of the sandwich structure, with mechanical properties as specified in Equations (30) and (31); (10,10) SWCNTs are considered as the reinforcement phase (Table 3). The mechanical properties of materials depend on the temperature. Table 5 presents the effect of the dimensionless thickness ratio \(L/h\) on the buckling load of a single layer CNTRC curved beam with various CNT volume fractions in the presence (or absence) of a thickness stretching effect \(\varepsilon_{zz}\), while keeping the opening angle \(\alpha=L/R\) equal to \(\pi/3\). Note that increased values of \(L/h\) result in lower values of the buckling load, under the same assumptions for the reinforcement distribution, volume fraction and possible stretching effects. In any case, the worst buckling response is observed for an FG-O reinforcement distribution within the material, whereas a FG-X distribution seems to yield the highest buckling loads for fixed values of \(L/h\), \(\varepsilon_{zz}\), \(V_{cnt}^{*}\). The stability of the curved beam increases significantly for higher values of \(V_{cnt}^{*}\), with a small variation in the buckling load, depending on whether \(\varepsilon_{zz}\) is assumed (or not) equal to zero. In Table 6, we account for the influence of opening angles \(\alpha\), boundary conditions, and CNT reinforcement patterns on the dimensionless critical buckling load of \((0^{\circ}/90^{\circ}/c/90^{\circ}/0^{\circ})\) \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multirow{2}{*}{_L/h_} & \multicolumn{4}{c}{**CC**} & \multicolumn{4}{c}{**SS**} \\ \cline{3-10}  & & \(V_{cnt}^{*}\)=12 & \(V_{cnt}^{*}\)=17 & \(V_{cnt}^{*}\)=28 & \(V_{cnt}^{*}\)=12 & \(V_{cnt}^{*}\)=17 & \(V_{cnt}^{*}\)=28 \\ \hline \multirow{10}{*}{UD} & Wu [6] & 0.0254 & 0.0296 & 0.0373 & 0.0070 & 0.0082 & 0.0107 \\  & Present & \(\varepsilon_{zz}=0\) & 0.0271 & 0.0319 & 0.0413 & 0.0071 & 0.0084 & 0.0110 \\  & & Present & & & & & & \\  & & \(\varepsilon_{zz}\
eq 0\) & 0.0267 & 0.0316 & 0.0410 & 0.0066 & 0.0080 & 0.0106 \\ \cline{2-10}  & 20 & [PERSON] [6] & 0.0070 & 0.0082 & 0.0107 & 0.0018 & 0.0021 & 0.0028 \\  & & Present & 0.0071 & 0.0084 & 0.0110 & 0.0018 & 0.0021 & 0.0028 \\  & & Present & \(\varepsilon_{zz}\
eq 0\) & 0.0069 & 0.0082 & 0.0108 & 0.0017 & 0.0020 & 0.0027 \\ \cline{2-10}  & 30 & [PERSON] [6] & 0.0031 & 0.0037 & 0.0049 & 0.0008 & 0.0009 & 0.0012 \\  & & Present & 0.0032 & 0.0038 & 0.0049 & 0.0008 & 0.0009 & 0.0012 \\  & & Present & & & & & & \\  & & \(\varepsilon_{zz}\
eq 0\) & 0.0031 & 0.0037 & 0.0049 & 0.0007 & 0.0008 & 0.0012 \\ \hline \multirow{10}{*}{FG} & \multirow{10}{*}{10} & Wu [6] & 0.0261 & 0.0305 & 0.0387 & 0.0072 & 0.0085 & 0.0111 \\  & Present & & 0.0271 & 0.0319 & 0.0413 & 0.0071 & 0.0084 & 0.0110 \\ \cline{1-1}  & & Present & & & & & & \\  & & \(\varepsilon_{zz}\
eq 0\) & 0.0267 & 0.0316 & 0.0410 & 0.0066 & 0.0079 & 0.0106 \\ \cline{1-1} \cline{2-10}  & \multirow{10}{*}{20} & Wu [6] & 0.0072 & 0.0085 & 0.0111 & 0.0018 & 0.0022 & 0.0029 \\  & & Present & & 0.0071 & 0.0084 & 0.0110 & 0.0018 & 0.0021 & 0.0028 \\  & & Present & & & & & & \\  & & \(\varepsilon_{zz}\
eq 0\) & 0.0069 & 0.0082 & 0.0108 & 0.0017 & 0.0020 & 0.0027 \\ \cline{2-10}  & & \multirow{10}{*}{30} & [PERSON] [6] & 0.0032 & 0.0039 & 0.0051 & 0.0008 & 0.0010 & 0.0013 \\  & & Present & & & & & & \\  & & \(\varepsilon_{zz}=0\) & 0.0032 & 0.0038 & 0.0049 & 0.0008 & 0.0010 & 0.0012 \\ \cline{2-10}  & & Present & & & & & & \\  & & \(\varepsilon_{zz}\
eq 0\) & 0.0031 & 0.0037 & 0.0049 & 0.0007 & 0.0009 & 0.0012 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparisons of dimensionless critical buckling loads for FG-CNTRC straight beams \(h_{c}\)/\(h_{f}\), \(V_{cnt}^{*}=0.12\).