## Appendix B
\[\begin{array}{c}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(1)}A_{11}(x_{r}) \bigg{)}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(1)}U(x_{r})\bigg{)}+A_{11} \Big{(}x_{p}\bigg{)}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(2)}U(x_{r})\bigg{)} -\frac{n^{2}A_{66}(x_{r})\mu(x_{p})}{R^{2}}\\ -\frac{nV(x_{p})}{R}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(1)}A_{12}(x_{r}) \bigg{)}-\frac{nA_{12}(x_{p})}{R}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(1)}V(x_ {r})\bigg{)}-\frac{nA_{66}(x_{r})}{R}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(1)} V(x_{r})\bigg{)}\\ +\frac{W(x_{p})}{R}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(1)}A_{12}(x_{r}) \bigg{)}+\frac{A_{12}(x_{p})}{R}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(1)}W(x_ {r})\bigg{)}-\overline{c}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(1)}D_{11}(x_ {r})\bigg{)}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(2)}W(x_{r})\bigg{)}\\ -\overline{c}D_{11}\Big{(}x_{p}\bigg{)}\bigg{(}\sum\limits_{r=1}^{N}\chi_{pr}^{(3)} W(x_{r})\bigg{)}  
\[+\frac{4\overline{c}^{2}n^{2}}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N} \chi_{pr}^{(1)}G_{66}(x_{\tau})\biggr{)}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr} ^{(1)}W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{4}G_{11}(x_{\tau})W(x_{ \tau})}{R^{4}}\] \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\] \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\] \[-\frac{n^{2}A_{66}(x_{\tau})W(x_{\tau})}{R^{2}}+\frac{\overline{c }W(x_{\tau})}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2)}D_{12}(x_{\tau} )\biggr{)}+\frac{2\overline{c}}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{( 1)}D_{12}(x_{\tau})\biggr{)}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(1)}W(x_ {\tau})\biggr{)}\] \[+\frac{2\overline{c}D_{12}(x_{\tau})}{R}\biggl{(}\sum\limits_{ \
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+A_{66}(x_{\tau})\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\biggl{(}\sum\limits_{ \
u=1}^{N}\chi_{pr}^{(1)}A_{66}(x_{\tau})\biggr{)}\biggl{(}\sum\limits_{\
u=1} ^{N}\chi_{pr}^{(1)}W(x_{\tau})\biggr{)}\] \[-2\overline{c}^{2}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(1) }G_{11}(x_{\tau})\biggr{)}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(3)}W(x_{ \tau})\biggr{)}-c^{2}G_{11}\biggl{(}x_{\tau}\biggr{)}\biggl{(}\sum\limits_{\
u =1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}-\frac{A_{11}(x_{\tau})W(x_{\tau})}{R ^{2}}\] \[-6\overline{c}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(1)}C_{66 }(x_{\tau})\biggr{)}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(1)}W(x_{\tau} )\biggr{)}-6\overline{c}C_{66}\biggl{(}x_{\tau}\biggr{)}\biggl{(}\sum\limits_{ \
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}\] \[+\frac{2\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(1)}\Phi_{x}(x_{\tau})\biggr{)}+\frac{2\overline {c}^{2}n^{2}\Phi_{x}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^ {(1)}G_{66}(x_{\tau})\biggr{)}\] \[-\frac{\overline{c}n^{2}F_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(1)}\Phi_{x}(x_{\tau})\biggr{)}-\frac{2\overline {c}n^{2}\Phi_{x}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(1 )}F_{66}(x_{\tau})\biggr{)}\] \[-\frac{2\overline{n}^{2}F_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(1)}\[PERSON]_{x}(x_{\tau})\biggr{)}+\frac{2\overline {c}^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^ {(1)}\[PERSON]_{x}(x_{\tau})\biggr{)}\] \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]0 \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]1 \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]2 (A9) \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]3 \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]4 \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]5 \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]6 \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]7 \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]8 \[+\frac{\overline{c}^{2}n^{2}W(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}G_{12}(x_{\tau})\biggr{)}+\frac{2\overline{c} ^{2}n^{2}G_{12}(x_{\tau})}{R^{2}}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2) }W(x_{\tau})\biggr{)}-\frac{\overline{c}^{2}n^{2}F_{66}(x_{\tau})W(x_{\tau})}{R ^{2}}\]9 \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]0 \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]1 \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]2 \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]3 \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]4 \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]5 \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]6 \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]7 \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]8 (10) \[+\frac{\overline{c}^{2}n^{2}G_{66}(x_{\tau})}{R^{2}}\biggl{(}\sum \limits_{\
u=1}^{N}\chi_{pr}^{(2)}W(x_{\tau})\biggr{)}+\frac{6\overline{c}^{2} C_{66}(x_{\tau})W(x_{\tau})}{R^{2}}-\frac{2\overline{c}^{2}D_{11}(x_{\tau})W(x_{ \tau})}{R^{3}}\]9 \[-\frac{n^{2}A_{66}(x_{\tau})W(x_{\tau})}{R^{2}}+\frac{\overline{c }W(x_{\tau})}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2)}D_{12}(x_{\tau} )\biggr{)}+\frac{2\overline{c}}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{( 1)}D_{12}(x_{\tau})\biggr{)}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(1)}W(x_ {\tau})\biggr{)}\]0 \[-\frac{n^{2}A_{66}(x_{\tau})W(x_{\tau})}{R^{2}}+\frac{\overline{c }W(x_{\tau})}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2)}D_{12}(x_{\tau} )\biggr{)}+\frac{2\overline{c}}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{( 1)}D_{12}(x_{\tau})\biggr{)}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(1)}W(x_ {\tau})\biggr{)}\]1 \[-\frac{n^{2}A_{66}(x_{\tau})W(x_{\tau})}{R^{2}}+\frac{\overline{c }W(x_{\tau})}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2)}D_{12}(x_{\tau} )\biggr{)}+\frac{2\overline{c}}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{( 1)}D_{12}(x_{\tau})\biggr{)}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(1)}W(x_ {\tau})\biggr{)}\]2 \[-\frac{n^{2}A_{66}(x_{\tau})W(x_{\tau})}{R^{2}}+\frac{\overline{c }W(x_{\tau})}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(2)}D_{12}(x_{\tau} )\biggr{)}+\frac{2\overline{c}}{R}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{( 1)}D_{12}(x_{\tau})\biggr{)}\biggl{(}\sum\limits_{\
u=1}^{N}\chi_{pr}^{(1)}W(x_ {\tau})\biggr{)}\]3 \[-\frac{\overline{c}^{2}nC_{66}\big{(}x_{p}\big{)}}{a}\!\left  
* [PERSON] et al.