## Appendix B Boundary Conditions  
The boundary conditions associated with the boundary value local problems in one-eighth of \(S\) are stated as follows:  
Problem \({}_{11}L:\)  
\[\begin{array}{l}{}_{11}\sigma_{12}^{(\mathrm{Y})}=0,\ _{11}\sigma_{13}^{( \mathrm{Y})}=0,\ _{11}M_{1}^{(\mathrm{Y})}=d_{1}\mid_{\{y_{1}=d_{1},\ y_{2},\ y_{3}\}},\\ {}_{11}\sigma_{21}^{(\mathrm{Y})}=0,\ _{11}M_{2}^{(\mathrm{Y})}=0,\ _{11}\sigma_{23}^{( \mathrm{Y})}=0\mid_{\{y_{1},\ y_{2}=d_{2},\ y_{3}\}},\\ {}_{11}\sigma_{31}^{(\mathrm{Y})}=0,\ _{11}\sigma_{31}^{(\mathrm{Y})}=0,\ _{11}M_{3}^{( \mathrm{Y})}=0\mid_{\{y_{1},\ y_{2},\ y_{3}=d_{3}\}}.\end{array}\] (A15)  
Problem \({}_{22}L:\)  
\[\begin{array}{l}{}_{22}M_{1}^{(\mathrm{Y})}=0,\ _{22}\sigma_{12}^{( \mathrm{Y})}=0,\ _{22}\sigma_{13}^{(\mathrm{Y})}=0\mid_{\{y_{1}=d_{1},\ y_{2},\ y_{3}\}},\\ {}_{22}\sigma_{21}^{(\mathrm{Y})}=0,\ _{22}\sigma_{23}^{(\mathrm{Y})}=0,\ _{22}M_{2}^{( \mathrm{Y})}=d_{2}\mid_{\{y_{1},\ y_{2}=d_{2},\ y_{3}\}},\\ {}_{22}\sigma_{31}^{(\mathrm{Y})}=0,\ _{22}\sigma_{32}^{(\mathrm{Y})}=0,\ _{22}M_{3}^{( \mathrm{Y})}=0\mid_{\{y_{1},\ y_{2},\ y_{3}=d_{3}\}}.\end{array}\] (A16)  
Problem \({}_{33}L:\)  
\[\begin{array}{l}{}_{33}M_{1}^{(\mathrm{Y})}=0,\ _{33}\sigma_{12}^{( \mathrm{Y})}=0,\ _{33}\sigma_{13}^{(\mathrm{Y})}=0\mid_{\{y_{1}=d_{1},\ y_{2},\ y_{3}\}},\\ {}_{33}\sigma_{21}^{(\mathrm{Y})}=0,\ _{33}M_{2}^{(\mathrm{Y})}=0,\ _{33}\sigma_{23}^{( \mathrm{Y})}=0\mid_{\{y_{1},\ y_{2}=d_{2},\ y_{3}\}},\\ {}_{33}\sigma_{31}^{(\mathrm{Y})}=0,\ _{33}\sigma_{32}^{(\mathrm{Y})}=0,\ _{33}M_{3}^{( \mathrm{Y})}=d_{3}\mid_{\{y_{1},\ y_{2},\ y_{3}=d_{3}\}}.\end{array}\] (A17)  
Problem \({}_{23}L:\)  
\[\begin{array}{l}{}_{23}M_{1}^{(\mathrm{Y})}=0,\ _{23}\sigma_{12}^{( \mathrm{Y})}=0,\ _{23}\sigma_{13}^{(\mathrm{Y})}=0\mid_{\{y_{1}=d_{1},\ y_{2},\ y_{3}\}},\\ {}_{23}M_{1}^{(\mathrm{Y})}=0,\ _{23}\sigma_{22}^{(\mathrm{Y})}=0,\ _{23}M_{3}^{( \mathrm{Y})}=d_{2}\mid_{\{y_{1},\ y_{2}=d_{2},\ y_{3}\}},\\ {}_{23}M_{1}^{(\mathrm{Y})}=0,\ _{23}M_{2}^{(\mathrm{Y})}=0,\ _{23}\sigma_{33}^{( \mathrm{Y})}=0\mid_{\{y_{1},\ y_{2},\ y_{3}=d_{3}\}}.\end{array}\] (A18)Problem \({}_{13}L:\)  
\[\begin{split}&{}_{13}\sigma_{11}^{(\mathrm{Y})}=0,\ _{13}M_{2}^{(\mathrm{Y})}=0,\ _{13}M_{3}^{(\mathrm{Y})}=d_{1}\ |_{\{y_{1}=d_{1},\ y_{2},\ y_{3}\}},\\ &{}_{13}\sigma_{21}^{(\mathrm{Y})}=0,\ _{13}M_{2}^{(\mathrm{Y})}=0,\ _{13} \sigma_{23}^{(\mathrm{Y})}=0\ |_{\{y_{1},\ y_{2}=d_{2},\ y_{3}\}},\\ &{}_{13}M_{1}^{(\mathrm{Y})}=0,\ _{13}M_{2}^{(\mathrm{Y})}=0,\ _{13} \sigma_{33}^{(\mathrm{Y})}=0\ |_{\{y_{1},\ y_{2},\ y_{3}=d_{3}\}}\.\end{split} \tag{134}\]  
Problem \({}_{12}L:\)  
\[\begin{split}&{}_{12}\sigma_{11}^{(\mathrm{Y})}=0,\ _{12}M_{3}^{(\mathrm{Y})}=0,\ _{12}M_{2}^{(\mathrm{Y})}=d_{1}\ |_{\{y_{1}=d_{1},\ y_{2},\ y_{3}\}},\\ &{}_{12}M_{1}^{(\mathrm{Y})}=0,\ _{12}\sigma_{22}^{(\mathrm{Y})}=0,\ _{12}M_{3}^{(\mathrm{Y})}=0\ |_{\{y_{1},\ y_{2}=d_{2},\ y_{3}\}},\\ &{}_{12}\sigma_{31}^{(\mathrm{Y})}=0,\ _{12}\sigma_{32}^{(\mathrm{Y})}=0,\ _{12}M_{3}^{(\mathrm{Y})}=0\ |_{\{y_{1},\ y_{2},\ y_{3}=d_{3}\}},\end{split} \tag{135}\]  
where \(I_{1}\), \(I_{2}\) and \(I_{3}\) are:  
\[\begin{split}& I_{1}=\{(y_{1},y_{2},y_{3})\in\mathbb{R}^{3}\ |\ y_{1}=\{0,\ l_{1}\},\ \ 0\leq y_{2}\leq l_{2},\ \ 0\leq y_{3}\leq l_{3}\},\\ & I_{2}=\{(y_{1},y_{2},y_{3})\in\mathbb{R}^{3}\ |\ 0\leq y_{1}\leq l_{1},\ \ y_{2}=\{0,\ l_{2}\},\ 0\leq y_{3}\leq l_{3}\}\ \text{and}\\ & I_{3}=\{(y_{1},y_{2},y_{3})\in\mathbb{R}^{3}\ |\ 0\leq y_{1}\leq l_{1},\ \ 0\leq y_{2}\leq l_{2},\ \ y_{3}=\{0,\ l_{3}\}\}.\end{split} \tag{136}\]