From c4c20c4da04e2103412533d86508e8e6a336e42b Mon Sep 17 00:00:00 2001 From: haidi Date: Thu, 28 Sep 2023 10:02:48 +0800 Subject: [PATCH] Update README.md --- README.md | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 416029b..18207ec 100644 --- a/README.md +++ b/README.md @@ -35,7 +35,9 @@ pip install . Please refer to [mech2d](https://doi.org/10.3390/molecules28114337) The polar plot of Young's modulus and Poisson's ratio is obtained by following equation: -$$ \begin{align*} + +$$ +\begin{align*} v_{zz} & = \frac{C_{12}}{C_{22}} \\ d_1 & = \frac{C_{11}}{C_{22}} + 1 - \frac{C_{11} C_{22} - C_{12}^2}{C_{22} C_{66}} \\ d_2 & = -\left(2 \frac{C_{12}}{C_{22}} - \frac{C_{11} C_{22} - C_{12}^2}{C_{22} C_{66}}\right) \\ @@ -44,7 +46,8 @@ Y_{zz} & = \frac{C_{11} C_{22} - C_{12}^2}{C_{22}} \\ \theta & \in [0, 2\pi] \text{ with 360 points} \\ E(\theta) & = \frac{Y_{zz}}{\cos(\theta)^4 + d_2 \cos(\theta)^2 \sin(\theta)^2 + d_3 \sin(\theta)^4} \\ V(\theta) & = \frac{v_{zz} \cos(\theta)^4 - d_1 \cos(\theta)^2 \sin(\theta)^2 + v_{zz} \sin(\theta)^4}{\cos(\theta)^4 + d_2 \cos(\theta)^2 \sin(\theta)^2 + d_3 \sin(\theta)^4} -\end{align*} $$ +\end{align*} +$$ ## Usage