This repository contains google colab based FEniCS implementation of the elastodynamics problem. This model will be further extended to include Physics Informed Neural Network (PINN) using Long Short-Term Memory (LSTM).
We use python 3.6.9 as the programming language. In this project we use the libraries :
- FEniCS 2019.1.0 (www.fenicsproject.org)
- Matplolib 3.1.2 (www.matplotlib.org)
- numpy 1.17.4 (www.numpy.org)
The solutions are stored in .pvd format, which can later be viewed with Paraview (www.paraview.org).
Simply clone the public repository:
git clone https://github.com/niravshah241/elastodynamics_LSTM_PINN.git
The domain is divided into
Above equation is solved using Finite Element Method in space and generalised-
The stress tensor
The normal force
The Boundary conditions are given by:
The initial conditions correspond to the body at continuous rest:
The corresponding weak form can be expressed as, find
The damping term
Rayleigh damping with specified coefficients
The velocity and displacement are approximated as:
At each time step the elastic enegy and Kinetic energy are givem by:
The energy transfer into or out of the system is given by:
The total energy of the system is the sum of all energies:
- Displacement evolution
Energy evolution | Von Mises stress evolution |
---|---|
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This code has been developed by [Nirav Shah] email.
@misc{elastodynamics_LSTM_PINN,
key = {ElastodynamicsLSTMPINN},
author = {Shah, N.V.},
title = {{Long Short Term Memory based Physics Informed Neural Network for elastodynamics problem, Version 0.1}},
month = July,
url = {https://github.com/niravshah241/elastodynamics_LSTM_PINN.git},
year = 2022
}
- FEniCS is freely available under the GNU LGPL, version 3.
- Matplotlib only uses BSD compatible code, and its license is based on the PSF license. Non-BSD compatible licenses (e.g., LGPL) are acceptable in matplotlib toolkits.
Accordingly, this code is freely available under the GNU LGPL, version 3 and BSD-license.
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