Stress On Mesh

#Physics

$\displaystyle F_{\text{through }A}=\int {A}\sigma(x,y) , \mathrm{d}A\approx \sum{i\in \text{edges that intersect }A}(\sigma_{i}a_{\text{voronoi }i})(\hat{d}_{i}\cdot \hat{n})$

• This is the total axial force through a plane $\displaystyle A$ of a body defined by a mesh
• $\displaystyle \hat{d}$ is unit direction of the mesh edge
• $\displaystyle \hat{n}$ is the normal of $\displaystyle A$
• $\displaystyle a_{\text{voronoi}}$ can be approximated as $\displaystyle \frac{1}{3}$ the area of the face areas incident to the edge