Model Mathematics

Elim11 = Tol a11

Elim22 = Tol a22

Elim33 = Tol a33

Elim12 = Tol a12

Elim13 = Tol a13

Elim23 = Tol a23

Sign12 = \{\begin{matrix} 1.0 if E12 \geq 0.0 \\ -1.0 otherwise \end{matrix}

Sign13 = \{\begin{matrix} 1.0 if E13 \geq 0.0 \\ -1.0 otherwise \end{matrix}

Sign23 = \{\begin{matrix} 1.0 if E23 \geq 0.0 \\ -1.0 otherwise \end{matrix}

Eabs12 = \{\begin{matrix} E12 if E12 \geq 0.0 \\ (-1.0) E12 otherwise \end{matrix}

Eabs13 = \{\begin{matrix} E13 if E13 \geq 0.0 \\ (-1.0) E13 otherwise \end{matrix}

Eabs23 = \{\begin{matrix} E23 if E23 \geq 0.0 \\ (-1.0) E23 otherwise \end{matrix}

Tdev11 = \{\begin{matrix} \frac{2.0 k11 E11}{{a11}^{b11}} if E11 ≦ 0.0 \\ \frac{k11 Elim11}{{(a11 - Elim11)}^{b11}} (2.0 + \frac{b11 Elim11}{a11 - Elim11}) + \frac{k11}{{(a11 - Elim11)}^{b11}} (2.0 + \frac{4.0 b11 Elim11}{a11 - Elim11} + \frac{b11 {Elim11}^{2.0} (b11 + 1.0)}{{(a11 - Elim11)}^{2.0}}) (E11 - Elim11) if E11 > Elim11 \\ \frac{k11 E11}{{(a11 - E11)}^{b11}} (2.0 + \frac{b11 E11}{a11 - E11}) otherwise \end{matrix}

Tdev22 = \{\begin{matrix} \frac{2.0 k22 E22}{{a22}^{b22}} if E22 ≦ 0.0 \\ \frac{k22 Elim22}{{(a22 - Elim22)}^{b22}} (2.0 + \frac{b22 Elim22}{a22 - Elim22}) + \frac{k22}{{(a22 - Elim22)}^{b22}} (2.0 + \frac{4.0 b22 Elim22}{a22 - Elim22} + \frac{b22 {Elim22}^{2.0} (b22 + 1.0)}{{(a22 - Elim22)}^{2.0}}) (E22 - Elim22) if E22 > Elim22 \\ \frac{k22 E22}{{(a22 - E22)}^{b22}} (2.0 + \frac{b22 E22}{a22 - E22}) otherwise \end{matrix}

Tdev33 = \{\begin{matrix} \frac{2.0 k33 E33}{{a33}^{b33}} if E33 ≦ 0.0 \\ \frac{k33 Elim33}{{(a33 - Elim33)}^{b33}} (2.0 + \frac{b33 Elim33}{a33 - Elim33}) + \frac{k33}{{(a33 - Elim33)}^{b33}} (2.0 + \frac{4.0 b33 Elim33}{a33 - Elim33} + \frac{b33 {Elim33}^{2.0} (b33 + 1.0)}{{(a33 - Elim33)}^{2.0}}) (E33 - Elim33) if E33 > Elim33 \\ \frac{k33 E33}{{(a33 - E33)}^{b33}} (2.0 + \frac{b33 E33}{a33 - E33}) otherwise \end{matrix}

Tdev12 = Sign12 \{\begin{matrix} \frac{k12 Elim12}{{(a12 - Elim12)}^{b12}} (2.0 + \frac{b12 Elim12}{a12 - Elim12}) + \frac{k12}{{(a12 - Elim12)}^{b12}} (2.0 + \frac{4.0 b12 Elim12}{a12 - Elim12} + \frac{b12 {Elim12}^{2.0} (b12 + 1.0)}{{(a12 - Elim12)}^{2.0}}) (Eabs12 - Elim12) if Eabs12 > Elim12 \\ \frac{k12 Eabs12}{{(a12 - Eabs12)}^{b12}} (2.0 + \frac{b12 Eabs12}{a12 - Eabs12}) otherwise \end{matrix}

Tdev13 = Sign13 \{\begin{matrix} \frac{k13 Elim13}{{(a13 - Elim13)}^{b13}} (2.0 + \frac{b13 Elim13}{a13 - Elim13}) + \frac{k13}{{(a13 - Elim13)}^{b13}} (2.0 + \frac{4.0 b13 Elim13}{a13 - Elim13} + \frac{b13 {Elim13}^{2.0} (b13 + 1.0)}{{(a13 - Elim13)}^{2.0}}) (Eabs13 - Elim13) if Eabs13 > Elim13 \\ \frac{k13 Eabs13}{{(a13 - Eabs13)}^{b13}} (2.0 + \frac{b13 Eabs13}{a13 - Eabs13}) otherwise \end{matrix}

Tdev23 = Sign23 \{\begin{matrix} \frac{k23 Elim23}{{(a23 - Elim23)}^{b23}} (2.0 + \frac{b23 Elim23}{a23 - Elim23}) + \frac{k23}{{(a23 - Elim23)}^{b23}} (2.0 + \frac{4.0 b23 Elim23}{a23 - Elim23} + \frac{b23 {Elim23}^{2.0} (b23 + 1.0)}{{(a23 - Elim23)}^{2.0}}) (Eabs23 - Elim23) if Eabs23 > Elim23 \\ \frac{k23 Eabs23}{{(a23 - Eabs23)}^{b23}} (2.0 + \frac{b23 Eabs23}{a23 - Eabs23}) otherwise \end{matrix}