[PLACEHOLDER] Stress Concentration Example

[PLACEHOLDER] Reference stub — demonstrates math, an interactive Plotly figure, and the PyVista embed pattern.

[PLACEHOLDER] This is the reference stub. It exists to prove the rendering pipeline (math, interactive plots, 3D scene embed), not to present real results. Copy this folder to start a real project, then replace every placeholder.

Math renders

A display equation, to prove LaTeX works. The stress-concentration factor relates the peak stress to a nominal stress:

\[ K_t \;=\; \frac{\sigma_{\max}}{\sigma_{\text{nom}}} \]

and, for a generic elliptical hole of semi-axes \(a\) (transverse) and root radius \(\rho\), a textbook form is:

\[ K_t \;=\; 1 + 2\sqrt{\frac{a}{\rho}} . \]

[PLACEHOLDER] Equations above are generic illustrations of math rendering — not a result. Replace with the relations relevant to your project.

Interactive plot renders

A trivial Plotly figure executed by the uv venv’s Jupyter kernel — proof the interactive plotting pipeline works. Rotate/zoom/hover to confirm it is live.

import plotly.graph_objects as go

# [PLACEHOLDER] trivial data — swap for real simulation output later.
x = [0, 1, 2, 3, 4, 5]
y = [v * v for v in x]

fig = go.Figure(go.Scatter(x=x, y=y, mode="lines+markers", name="[PLACEHOLDER]"))
fig.update_layout(
    template="plotly_white",
    margin=dict(l=50, r=20, t=30, b=45),
    xaxis_title="[PLACEHOLDER] x",
    yaxis_title="[PLACEHOLDER] y",
)
fig

Figure 1: [PLACEHOLDER] Trivial Plotly figure (y = x²) — replace with real post-processed data.

Interactive 3D result (PyVista)

This is where a rotatable/zoomable PyVista scene goes. No scene exists yet, so a placeholder box is shown. The embed snippet below is the copy-paste pattern.

[ PLACEHOLDER ] PyVista scene

No scene exported yet — generate one offline and drop it in assets/scenes/, then replace this box with the commented <iframe> below.

Write-up

[PLACEHOLDER] Explanatory text, method, mesh details, and discussion go here.