/matrix-analysis-python

Primary LanguagePython

Matrix Structural Analysis Project

(Python Version)

This repository contains a Python implementation of a matrix structural analysis for a 3D truss structure. The project includes the ability to calculate node displacements, reaction forces, and element forces for a given structure based on user-defined inputs.

Demo of the project

Project Structure

  • main.py: The main entry point for the program. It contains the core logic to set up and solve the structural analysis.
  • swingset.py: A script that executes the analysis and handles output formatting and debugging.
  • plot.py: Contains the function for plotting the 3D structure based on node coordinates and element connectivity.
  • analysis.py: Contains helper functions for calculating element stiffness matrices and transformation matrices.

Features

  • Calculate nodal displacements under given loads.
  • Compute reaction forces at fixed supports.
  • Determine internal forces in each element.
  • Plot the 3D structure for visual analysis.

Requirements

  • Python 3.x
  • NumPy
  • Matplotlib

You can install the required packages using the following command:

pip install numpy matplotlib

Usage

  1. Running the Analysis:

    • Ensure that the necessary files (main.py, swingset.py, plot.py, analysis.py) are in the same directory.
    • Run the main script to execute the analysis and view the results: 
      python main.py

  2. Debugging:

    • The script outputs detailed variables and matrices used in the analysis. If additional debugging information is needed, you can enable more print statements in swingset.py or add to the debug.py file.

  3. Plotting:

    • The structure can be visualized by running the plot function in plot.py. The structure is plotted in 3D using Matplotlib, with nodes and elements clearly indicated.

Screenshots

Screenshot 1: Node Deflections Output

Node Deflections Output

(An example output of deflections)

Screenshot 2: 3D Structure Plot

3D Structure Plot

(Plot of the structure)

How It Works

  1. Input Setup:

    • Define the number of nodes (nnodes) and elements (nele).
    • Set up node coordinates and element connectivity (coord and ends).
    • Specify external forces and fixity conditions.

  2. Matrix Assembly:

    • Local stiffness matrices are computed for each element using the estiff function from analysis.py.
    • Transformation matrices are calculated to account for the orientation of each element using the etran function.
    • Global stiffness matrix is assembled by aggregating local matrices.

  3. Solving:

    • The global stiffness matrix is partitioned into free and fixed degrees of freedom.
    • The displacement vector for free nodes is solved using linear algebra.
    • Reaction forces and internal element forces are calculated.

  4. Output:

    • The script outputs node displacements and reaction forces.
    • The structure is visualized using Matplotlib.

Future Enhancements

  • Web Application: Plan to develop a web app that allows users to interactively plot structures and input material properties.
  • Additional Debugging: Incorporate a more robust debugging mechanism, potentially via a debug.py file to hold additional variable outputs.