https://github.com/juliareach/setpropagation-fem-juliacon21

Computing Reachable Sets of Semi-Discrete Solid Dynamics Equations with ReachabilityAnalysis.jl
https://github.com/juliareach/setpropagation-fem-juliacon21

finite-element-method heat-transfer numerical-verification reachability-analysis structural-dynamics

Last synced: 2 months ago
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Computing Reachable Sets of Semi-Discrete Solid Dynamics Equations with ReachabilityAnalysis.jl

• Host: GitHub
• URL: https://github.com/juliareach/setpropagation-fem-juliacon21
• Owner: JuliaReach
• License: mit
• Created: 2021-09-13T19:19:29.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2023-03-31T14:22:47.000Z (about 2 years ago)
• Last Synced: 2024-12-26T08:12:52.611Z (4 months ago)
• Topics: finite-element-method, heat-transfer, numerical-verification, reachability-analysis, structural-dynamics
• Language: TeX
• Homepage: http://juliareach.com
• Size: 46 MB
• Stars: 1
• Watchers: 5
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Computing Reachable Sets of Semi-Discrete Solid Dynamics Equations with ReachabilityAnalysis.jl

by [Jorge M. Pérez Zerpa](https://github.com/jorgepz) (Instituto de Estructuras y Transporte, Facultad de Ingeniería, UdelaR, Montevideo, Uruguay), [Marcelo Forets](https://github.com/mforets) (Depto. de Matemática y Aplicaciones, CURE, UdelaR, Maldonado, Uruguay) and

[Daniel Freire Caporale](https://github.com/dfcaporale) (Instituto de Física, Facultad de Ciencias, UdelaR, Montevideo, Uruguay).

[![status](https://proceedings.juliacon.org/papers/24a082818ba9447244932e21d16da342/status.svg)](https://proceedings.juliacon.org/papers/24a082818ba9447244932e21d16da342)

[![DOI](https://zenodo.org/badge/406100282.svg)](https://zenodo.org/badge/latestdoi/406100282)

[JuliaCon Proceedings (pdf) of Computing Reachable Sets of Semi-Discrete Solid Dynamics Equations with ReachabilityAnalysis.jl

](https://proceedings.juliacon.org/papers/10.21105/jcon.00095)

## Presentation

[![JuliaCon 2021 video](https://img.youtube.com/vi/MQM9U0hiLks/0.jpg)](https://youtu.be/MQM9U0hiLks)

## Extended Abstract

During the review process, the pdf is automatically generated by `whedon`, see: https://github.com/JuliaCon/proceedings-review/issues/95

## Publication

[JuliaCon Proceedings (pdf) of Computing Reachable Sets of Semi-Discrete Solid Dynamics Equations with ReachabilityAnalysis.jl

](https://proceedings.juliacon.org/papers/10.21105/jcon.00095)

See Forets, Marcelo, Daniel Freire Caporale, and Jorge M. Pérez Zerpa. ["Combining set propagation with finite element methods for time integration in transient solid mechanics problems."](https://www.sciencedirect.com/science/article/abs/pii/S0045794921002212) Computers & Structures 259 (2022): 106699.

The pre-print is available here: https://arxiv.org/abs/2105.05841

## Implementation

See https://github.com/JuliaReach/ReachabilityAnalysis.jl

## Examples repository

See https://github.com/JuliaReach/SetPropagation-FEM-Examples

## Minimal example

We solve the system of two degrees of freedom loaded with a Heaviside step function subject to

Rayleigh damping shown in the diagram below.



Given the FEM assembled matrices, the range of variation of the external loads is 10\% around the nominal value 1.

Initial displacements and velocities for both masses belong to the interval `[-0.5, 0.5]`.

The initial-value problem is instantiated and homogeneized as described in [1].



To illustrate the flexibility of our approach, two algorithm choices are considered, both relying on support functions [7] (`LGG09` algorithm). `solA` contains the flowpipe efficiently computed along box directions. To improve the accuracy, `solB` is computed using octagonal template directions.





## References

See https://github.com/JuliaCon/proceedings-review/issues/95