# 3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions
## 5 Conclusions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{R_{a}/h}\) & \(\mathbf{2}\) & \(\mathbf{4}\) & \(\mathbf{10}\) & \(\mathbf{50}\) & \(\mathbf{100}\) \\ \hline \multicolumn{6}{c}{\(\mathcal{M}\) at \((\alpha=a/2,\beta=b/2;\hat{z}=h/2)[-]\)} \\ \hline \multicolumn{6}{c}{\(3\)D(\(\mathcal{M}_{a}\))} \\ \hline \(3\)D(\(\mathcal{M}_{c},1D\)) & \(0.5000\) & \(0.5000\) & \(0.5000\) & \(0.5000\) & \(0.5000\) \\ \(3\)D(\(\mathcal{M}_{c},1D\)) & \(0.2087\) & \(0.2087\) & \(0.2087\) & \(0.2087\) & \(0.2087\) \\ \(3\)D(\(\mathcal{M}_{c},3D\)) & \(0.0612\) & \(0.1376\) & \(0.1933\) & \(0.2080\) & \(0.2085\) \\ \multicolumn{6}{c}{\(v\) at \((\alpha=a/2,\beta=0;\hat{z}=h/3)\) [\(10^{-3}\) mm]} \\ \hline \(3\)D(\(\mathcal{M}_{a}\)) & \(-3.894\) & \(-2.822\) & \(-1.076\) & \(1.741\) & \(1.182\) \\ \(3\)D(\(\mathcal{M}_{c},1D\)) & \(-1.004\) & \(-0.628\) & \(0.4564\) & \(1.626\) & \(1.003\) \\ \(3\)D(\(\mathcal{M}_{c},3D\)) & \(0.2033\) & \(-0.1980\) & \(0.5091\) & \(1.625\) & \(1.003\) \\ \multicolumn{6}{c}{\(w\) at \((\alpha=a/2,\beta=b/2;\hat{z}=h/2)\) [\(10^{-3}\) mm]} \\ \hline \(3\)D(\(\mathcal{M}_{a}\)) & \(4.294\) & \(9.003\) & \(24.12\) & \(59.21\) & \(58.93\) \\ \(3\)D(\(\mathcal{M}_{c},1D\)) & \(3.366\) & \(7.349\) & \(18.73\) & \(38.36\) & \(36.02\) \\ \(3\)D(\(\mathcal{M}_{c},3D\)) & \(2.910\) & \(6.711\) & \(18.31\) & \(38.31\) & \(36.00\) \\ \multicolumn{6}{c}{\(\sigma_{zz}\) at \((\alpha=a/2,\beta=b/2;\hat{z}=h/3)\) [\(\mathrm{kPa}\)]} \\ \hline \(3\)D(\(\mathcal{M}_{a}\)) & \(-337.9\) & \(-31.28\) & \(-0.2497\) & \(6.395\) & \(4.422\) \\ \(3\)D(\(\mathcal{M}_{c},1D\)) & \(-32.33\) & \(35.10\) & \(10.25\) & \(5.996\) & \(3.714\) \\ \(3\)D(\(\mathcal{M}_{c},3D\)) & \(85.74\) & \(45.62\) & \(10.43\) & \(5.991\) & \(3.713\) \\ \multicolumn{6}{c}{\(\sigma_{\beta z}\) at \((\alpha=a/2,\beta=0;\hat{z}=2h/3)\) [\(\mathrm{kPa}\)]} \\ \hline \(3\)D(\(\mathcal{M}_{a}\)) & \(240.7\) & \(125.3\) & \(61.39\) & \(-8.396\) & \(-9.287\) \\ \(3\)D(\(\mathcal{M}_{c},1D\)) & \(83.57\) & \(25.04\) & \(7.627\) & \(-17.21\) & \(-12.08\) \\ \(3\)D(\(\mathcal{M}_{c},3D\)) & \(13.41\) & \(3.374\) & \(5.225\) & \(-17.22\) & \(-12.08\) \\ \multicolumn{6}{c}{\(\epsilon_{\mathrm{ax}}\) at \((\alpha=a/2,\beta=b/2;\hat{z}=h)\) [\(10^{-6}\)]} \\ \hline \(3\)D(\(\mathcal{M}_{a}\)) & \(0.5547\) & \(-0.8651\) & \(-1.008\) & \(-2.249\) & \(-3.381\) \\ \(3\)D(\(\mathcal{M}_{c},1D\)) & \(-1.988\) & \(-3.376\) & \(-3.732\) & \(-5.260\) & \(-6.114\) \\ \(3\)D(\(\mathcal{M}_{c},3D\)) & \(-3.912\) & \(-4.182\) & \(-3.909\) & \(-5.268\) & \(-6.116\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Fourth benchmark, sandwich spherical shell panel with an FGM core subject to an external moisture content applied to the top and bottom surfaces. The results of all the 3D models consider \(N=3\) and \(NL=300\). **Author Contributions:** Data curation, R.T.; Formal analysis, S.B. and R.T.; Methodology, S.B. ; Software, S.B. ; Supervision, S.B. ; Validation, R.T.; Writing--original draft, R.T. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Conflicts of Interest:** The authors declare no conflict of interest.