Add Example for Dynamic Analysis of single pile subjected to lateral spreading

[AntroxEV]

Hello, we added a full example of the dynamic simulation of a single pile subjected to lateral spreading under seismic loading. The p-y relationship is following Franke and Rollins [1] hybrid spring model. Results obtained in OpenseesPy are verified against numerical and experimental results reported in [1] and [2].

1. Franke, K.W. and Rollins, K.M. (2013). “Simplified Hybrid p-y Spring Model for Liquefied Soils.” Journal of Geotechnical and Geoenvironmental Engineering, 139(4), 564–576. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000750 <https://doi.org/10.1061/(ASCE)GT.1943-5606.0000750>_.
2. Abdoun, T., Dobry, R., O'Rourke, T.D., and Goh, S.H. (2003).
   “Pile Response to Lateral Spreads: Centrifuge Modeling.”
   Journal of Geotechnical and Geoenvironmental Engineering, 129(10),
   869–878.
   https://doi.org/10.1061/(ASCE)1090-0241(2003)129:10(869) <https://doi.org/10.1061/(ASCE)1090-0241(2003)129:10(869)>_.

We added:

• a MWE script of this example (*py)
• a folder LATERALSPREAD including the time-histories used for the simulation
• RST file for web page
• GIFs and plot for the post-processing shown in the web page too

We hope this example can be published under the Example section of the documentation.
Many thanks

[Copilot]

Copilot review overview

🟡 Changes recommended

The simulation has incorrect depth-data alignment, missing default pile mass, and invalid bending-moment element access.

Review effort: Balanced
Findings: 5 · 2 · 2

Open (9)

• Resolve bundled record paths relative to the script · New
• Include pile mass in the Euler-Bernoulli model · New
• Include mass in free Euler-Bernoulli pile segments · New
• Resolve the second record path relative to the script · New
• Record bending moments using valid element tags · New
• Align loaded maxima with depth nodes · New
• Avoid out-of-range access at phi equals 38 · New
• Add new page to the Examples documentation index · New
• Remove leading dash from standalone animation · New

What changed in this PR

Adds a geotechnical example demonstrating dynamic monopile response to liquefaction-induced lateral spreading.

Changes:

• Adds the OpenSeesPy simulation and post-processing animations.
• Documents the model, references, and results.
• Describes the bundled displacement histories.

File	Description
src/​DynamicPYpile.rst	Adds the example documentation page.
pyExamples/​PilewithDynamicPY_FRANKE_Abdoun2003_MWE.py	Implements the dynamic pile analysis.
pyExamples/​LATERALSPREAD/​readme.md	Describes the displacement-history data.

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