## 4 Numerical Results and Discussion
### Parametric Study
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **R/a** & _a/h_ & **Method** & \multicolumn{6}{c}{\(E_{1}\)/\(E_{2}\)} \\ \cline{3-10}  & & & **3** & **10** & **20** & **30** & **40** & **50** \\ \hline \multirow{6}{*}{\(w^{*}\)} & \multirow{3}{*}{10} & BDM & 32.259 & 19.215 & 12.731 & 9.620 & 7.755 & 6.504 \\  & & GDQ & 31.795 & 18.864 & 12.544 & 9.514 & 7.692 & 6.466 \\ \cline{2-10}  & & \multirow{3}{*}{50} & BDM & 13.260 & 5.632 & 3.059 & 2.091 & 1.587 & 1.277 \\  & & GDQ & 13.344 & 5.678 & 3.086 & 2.111 & 1.601 & 1.289 \\ \cline{2-10}  & & \multirow{3}{*}{100} & BDM & 4.356 & 1.631 & 0.834 & 0.554 & 0.414 & 0.329 \\  & & GDQ & 4.357 & 1.635 & 0.839 & 0.559 & 0.4177 & 0.332 \\ \cline{2-10}  & & \multirow{3}{*}{20} & BDM & 43.818 & 34.616 & 30.074 & 27.493 & 25.597 & 24.062 \\  & & GDQ & 42.631 & 32.968 & 28.419 & 25.954 & 24.192 & 22.785 \\ \cline{2-10}  & & \multirow{3}{*}{50} & BDM & 37.065 & 25.627 & 20.850 & 18.653 & 17.263 & 16.240 \\  & & GDQ & 37.146 & 25.559 & 20.728 & 18.520 & 17.132 & 16.116 \\ \cline{2-10}  & & \multirow{3}{*}{100} & BDM & 35.240 & 23.015 & 18.047 & 15.883 & 14.585 & 13.674 \\  & & GDQ & 36.173 & 24.169 & 19.235 & 17.042 & 15.701 & 14.742 \\ \hline \multirow{6}{*}{\(\sigma_{x}{}^{*}\)} & \multirow{3}{*}{20} & BDM & 875.1 & 1245.6 & 1395.2 & 1459.5 & 1496.1 & 1519.9 \\  & & GDQ & 886.2 & 1264.1 & 1413.8 & 1477.5 & 1513.6 & 1537.1 \\ \cline{2-10}  & & \multirow{3}{*}{50} & BDM & 1550.2 & 1865.4 & 1867 & 1836.2 & 1809.6 & 1788.7 \\ \cline{2-10}  & & GDQ & 1555.8 & 1883.5 & 1889.3 & 1859.8 & 1833.7 & 1813.1 \\ \cline{2-10}  & & \multirow{3}{*}{100} & BDM & 1559 & 1798.8 & 1792.4 & 1765.9 & 1743.5 & 1725.8 \\  & & GDQ & 1554.9 & 1802.4 & 1803.4 & 1781.6 & 1762.4 & 1747 \\ \cline{2-10}  & & \multirow{3}{*}{20} & BDM & 699.61 & 927.91 & 956.36 & 931.67 & 895.94 & 858.31 \\  & & GDQ & 720.6 & 972.1 & 1011.4 & 991.6 & 958.5 & 922.4 \\ \cline{2-10}  & & \multirow{3}{*}{50} & BDM & 1998.1 & 2828.2 & 3033.5 & 3041.7 & 2998.1 & 2936.2 \\  & & GDQ & 1993.2 & 2839 & 3052.9 & 3065.7 & 3025 & 2965.3 \\ \cline{2-10}  & & \multirow{3}{*}{100} & BDM & 4140.5 & 5968.8 & 6481.1 & 6559.9 & 6519.6 & 6434.3 \\ \cline{2-10}  & & GDQ & 4059.6 & 5843.3 & 6328 & 6388.9 & 6334.7 & 6237.9 \\ \hline \multirow{6}{*}{\(\sigma_{y}{}^{*}\)} & \multirow{3}{*}{20} & BDM & 361.159 & 190.887 & 119.383 & 87.688 & 69.430 & 57.484 \\  & & GDQ & 357.635 & 187.504 & 117.347 & 86.424 & 68.601 & 56.918 \\ \cline{2-10}  & & \multirow{3}{*}{50} & BDM & 409.137 & 127.946 & 54.639 & 32.178 & 22.032 & 16.464 \\ \cline{1-1}  & & GDQ & 412.912 & 129.886 & 55.701 & 32.898 & 22.574 & 16.899 \\ \cline{1-1} \cline{2-10}  & & \multirow{3}{*}{100} & BDM & 265.097 & 51.627 & 14.368 & 6.362 & 3.601 & 2.383 \\ \cline{1-1}  & & GDQ & 264.017 & 52.361 & 15.190 & 7.074 & 4.208 & 2.906 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Normalized central deflectionsVariations of normalized central deflection, \(w^{\star}\), and stresses, \(\sigma_{x}{}^{*}\), of spherical (R/\(a=10\)) shell and two cylindrically curved panels for various length-to-thickness, \(a/h\) ratios under uniform loading are presented in Figure 3 for antisymmetric cross-ply [\(0^{\circ}/90^{\circ}\)] and Figure 4 for symmetric [\(0^{\circ}/90^{\circ}/0^{\circ}\)] lamination, respectively. The transverse shear deformation curves of the [\(0^{\circ}/90^{\circ}\)] spherical and cylindrical panel, with R\({}_{2}\rightarrow\infty\), are almost the same for the whole range of \(a/h\) ratio in the BDM method given in Figure 3a, as has already been observed in the case of the mixed simply supported boundary conditions in Reference [30]. While there is a relative difference between the BDM and GDQ methods for [\(0^{\circ}/90^{\circ}\)] spherical and cylindrical panels, normalized central deflection, \(w^{\star}\), and stress, \(\sigma_{x}{}^{*}\), curves have similar characteristics for both methods.