The project is about finding beam deflection using numerical methods and machine learning approach to compare the results
Overview
This project demonstrates how numerical methods and machine learning can be applied to solve real-world engineering problems. Specifically, it focuses on solving the beam deflection equation:
where represents the deflection (in meters). This equation models the deflection of a beam under load, accounting for stiffness, material resistance, and external forces.
Motivation
In structural engineering, predicting and analyzing beam deflection is critical to ensure safety and optimal design. While numerical methods have been the standard for such calculations, machine learning offers a modern approach to predict solutions efficiently based on prior data, making it suitable for more complex cases.
Objectives
Solve the beam deflection equation using:
Bisection Method
False Position Method
Fixed Point Iteration Method
Newton-Raphson Method
Train a machine learning model to predict deflection based on load parameters.
Compare the results from numerical methods and machine learning predictions with the exact solution.
Methods
- Bisection Method
Divides the interval into two halves and iteratively narrows the range containing the root.
Guarantees convergence if .
- False Position Method
Uses a straight-line approximation between two points to estimate the root.
- Fixed Point Iteration Method
Transforms the equation into and iteratively converges to the root.
- Newton-Raphson Method
Uses the tangent at a current guess to rapidly converge to the root.
- Machine Learning Model
Implements a regression model to predict deflection using data generated from the equation.
Dependencies
Python 3.8+
Libraries:
🔸 numpy
🔸 matplotlib
🔸 scipy
🔸 sklearn
🔸 tensorflow (or pytorch, optional for ML)
Install dependencies using:
pip install numpy matplotlib scipy scikit-learn tensorflow
How to Run
Clone the repository:
git clone https://github.com/yourusername/beam-deflection-analysis.git cd beam-deflection-analysis
Run numerical methods:
python numerical_methods.py
Train and test the machine learning model:
python ml_model.py
Project Structure
# beam-deflection-analysis/
│
├── numerical_methods.py # Contains Python implementations of 4 numerical methods
├── ml_model.py # Machine learning model for deflection prediction
├── README.md # Project documentation
├── requirements.txt # Dependencies
└── results/ # Results and comparison plotsResults
The project compares the following aspects:
Accuracy of numerical methods vs. machine learning.
Convergence speed for numerical methods.
Prediction error for machine learning.
Future Work
Expand the project to handle more complex equations, e.g., higher-order beam models.
Integrate neural networks for predicting deflection under varying material properties.
Contributors