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Merge pull request #601 from DLR-SL/develop
merge develop into master for 3.1 release
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5 changes: 5 additions & 0 deletions
5
documentation/equations/Q_EngineeringConstants_orthotropicShell.tex
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Q_{11}=\frac{E_1}{1-\nu_{12}\nu_{21}} \; , \quad | ||
Q_{22}=\frac{E_2}{1-\nu_{12}\nu_{21}} \; , \quad | ||
\newline | ||
Q_{12}=\frac{\nu_{12} E_2}{1-\nu_{12}\nu_{21}} = \frac{\nu_{21} E_1}{1-\nu_{12}\nu_{21}} \; , \quad | ||
Q_{33}=G_{12} |
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\frac{\nu_{ij}}{E_i}=\frac{\nu_{ji}}{E_j} |
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20
documentation/equations/strain_stress_orthotropicShell.tex
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\begin{pmatrix} | ||
\varepsilon_1 \\ | ||
\varepsilon_2 \\ | ||
\gamma_{12} | ||
\end{pmatrix} | ||
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= | ||
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\begin{bmatrix} | ||
\frac{1}{E_1} & -\frac{\nu_{21}}{E_2} & 0 \\ | ||
-\frac{\nu_{12}}{E_1}& \frac{1}{E_2} & 0 \\ | ||
0 & 0 & \frac{1}{G_{12}} \\ | ||
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\end{bmatrix} | ||
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\begin{pmatrix} | ||
\sigma_1 \\ | ||
\sigma_2 \\ | ||
\tau_{12} | ||
\end{pmatrix} |
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30 changes: 30 additions & 0 deletions
30
documentation/equations/strain_stress_orthotropicSolid.tex
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\begin{pmatrix} | ||
\varepsilon_1 \\ | ||
\varepsilon_2 \\ | ||
\varepsilon_3 \\ | ||
\gamma_{23} \\ | ||
\gamma_{31} \\ | ||
\gamma_{12} | ||
\end{pmatrix} | ||
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||
|
||
|
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= | ||
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\begin{bmatrix} | ||
\frac{1}{E_1} & -\frac{\nu_{21}}{E_2} & -\frac{\nu_{31}}{E_3} & 0 & 0 & 0 \\ | ||
-\frac{\nu_{12}}{E_1}& \frac{1}{E_2} & -\frac{\nu_{32}}{E_3} & 0 & 0 & 0 \\ | ||
-\frac{\nu_{13}}{E_1}& -\frac{\nu_{23}}{E_2} & \frac{1}{E_3} & 0 & 0 & 0 \\ | ||
0 & 0 & 0 & \frac{1}{G_{23}} & 0 & 0 \\ | ||
0 & 0 & 0 & 0 & \frac{1}{G_{31}} & 0 \\ | ||
0 & 0 & 0 & 0 & 0 & \frac{1}{G_{12}} \\ | ||
\end{bmatrix} | ||
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||
\begin{pmatrix} | ||
\sigma_1 \\ | ||
\sigma_2 \\ | ||
\sigma_3 \\ | ||
\tau_{23}\\ | ||
\tau_{31}\\ | ||
\tau_{12} | ||
\end{pmatrix} |
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30 changes: 30 additions & 0 deletions
30
documentation/equations/stress_strain_anisotropicShell.tex
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\begin{pmatrix} | ||
\sigma_1 \\ | ||
\sigma_2 \\ | ||
\tau_{12} | ||
\end{pmatrix} | ||
|
||
= | ||
|
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\begin{bmatrix} | ||
Q_{11} & Q_{12} & Q_{13} \\ | ||
& Q_{22} & Q_{23} \\ | ||
\text{symm.} & & Q_{33} | ||
\end{bmatrix} | ||
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||
\left( | ||
\begin{pmatrix} | ||
\varepsilon_1 \\ | ||
\varepsilon_2 \\ | ||
\gamma_{12} | ||
\end{pmatrix} | ||
- | ||
\left( T - T_{\text{ref}} \right ) | ||
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\begin{pmatrix} | ||
\text{thermalExpansionCoeff}_1 \\ | ||
\text{thermalExpansionCoeff}_2 \\ | ||
\text{thermalExpansionCoeff}_{12} | ||
\end{pmatrix} | ||
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||
\right ) |
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42 changes: 42 additions & 0 deletions
42
documentation/equations/stress_strain_anisotropicSolid.tex
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@@ -0,0 +1,42 @@ | ||
\begin{pmatrix} | ||
\sigma_1 \\ | ||
\sigma_2 \\ | ||
\sigma_3 \\ | ||
\tau_{23}\\ | ||
\tau_{31}\\ | ||
\tau_{12} | ||
\end{pmatrix} | ||
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= | ||
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\begin{bmatrix} | ||
C_{11} & C_{12} & C_{13} & C_{14} & C_{15} & C_{16} \\ | ||
& C_{22} & C_{23} & C_{24} & C_{25} & C_{26} \\ | ||
& & C_{33} & C_{34} & C_{35} & C_{36} \\ | ||
& & & C_{44} & C_{45} & C_{46} \\ | ||
& \text{symm.} & & & C_{55} & C_{56} \\ | ||
& & & & & C_{66} | ||
\end{bmatrix} | ||
|
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\left( | ||
\begin{pmatrix} | ||
\varepsilon_1 \\ | ||
\varepsilon_2 \\ | ||
\varepsilon_3 \\ | ||
\gamma_{23} \\ | ||
\gamma_{31} \\ | ||
\gamma_{12} | ||
\end{pmatrix} | ||
- | ||
\left( T - T_{\text{ref}} \right ) | ||
|
||
\begin{pmatrix} | ||
\text{thermalExpansionCoeff}_1 \\ | ||
\text{thermalExpansionCoeff}_2 \\ | ||
\text{thermalExpansionCoeff}_3 \\ | ||
\text{thermalExpansionCoeff}_{23} \\ | ||
\text{thermalExpansionCoeff}_{31} \\ | ||
\text{thermalExpansionCoeff}_{12} | ||
\end{pmatrix} | ||
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||
\right ) |
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33 changes: 33 additions & 0 deletions
33
documentation/equations/stress_strain_orthotropicShell.tex
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@@ -0,0 +1,33 @@ | ||
\begin{pmatrix} | ||
\sigma_1 \\ | ||
\sigma_2 \\ | ||
\tau_{12} | ||
\end{pmatrix} | ||
|
||
= | ||
|
||
\begin{bmatrix} | ||
Q_{11} & Q_{12} & 0 \\ | ||
Q_{12}& Q_{22} & 0 \\ | ||
0 & 0 & Q_{33} \\ | ||
\end{bmatrix} | ||
|
||
\left( | ||
\begin{pmatrix} | ||
\varepsilon_1 \\ | ||
\varepsilon_2 \\ | ||
\gamma_{12} | ||
\end{pmatrix} | ||
|
||
- | ||
\left( T - T_{\text{ref}} \right ) | ||
|
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\begin{pmatrix} | ||
\text{thermalExpansionCoeff}_1 \\ | ||
\text{thermalExpansionCoeff}_2 \\ | ||
0 \\ | ||
|
||
\end{pmatrix} | ||
|
||
|
||
\right ) |
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