2D Truss Solver (Matrix Stiffness Method)

Python implementation of a planar truss solver for strength-of-materials coursework. The code reads node/element/material data from CSV files, assembles the global stiffness matrix, solves for nodal displacements and support reactions, and reports axial forces, stresses, and material phase for each member.

Features

• Linear-elastic 2D truss analysis using the matrix stiffness method (NumPy)
• CSV-driven inputs for nodes, elements, and materials; easy to edit for new cases
• Computes nodal displacements, support reactions, axial forces, stresses, and state (tension/compression)
• Flags plastic/fracture phases based on yield/ultimate stress limits
• Text tables generated via tabulate and saved to io/result.txt
• Modular layout (io/, model/, solver/) for simple extension or replacement of components

Project Layout

• main.py — orchestrates reading inputs, assembling, solving, and writing results
• io/reader.py — loads CSV data from io/
• io/writer.py — formats and writes result tables to io/result.txt
• model/ — core classes: Node, Element, Material
• solver/ — assembly (assembly.py), boundary conditions (boundary.py), and linear solution (solve.py)
• io/*.csv — sample datasets for nodes, elements, and material properties

Input File Formats (CSV)

• io/nodes_input.csv
  • Columns: ID, x, y, F_x, F_y, constrained_x, constrained_y
  • constrained_*: 1 for fixed DOF, 0 for free. Use consistent units for forces and lengths.
• io/elements_input.csv
  • Columns: ID, node_1, node_2, cross_sectional_area, material
  • material must match a name in material.csv; area in square meters.
• io/material.csv
  • Columns: name, E, S_y, S_u
  • E in GPa; S_y and S_u in MPa. Values are converted to Pascals internally.

Requirements

• Python 3.9+
• Packages: numpy, tabulate (see requirements.txt)

How to Run

From the directory that contains the mom_project folder:

python -m venv .venv
.venv\Scripts\activate
pip install -r mom_project/requirements.txt
python -m mom_project.main

After execution, open mom_project/io/result.txt to view:

• Nodal displacements (Ux, Uy)
• Support reactions (Rx, Ry) at constrained DOFs
• Element axial forces, stresses, tension/compression state, and phase (Elastic/Plastic/Fracture)

Sample Output (truncated)

Nodal Displacements (Ux, Uy):
|   Node |           Ux |           Uy |
|      3 | -2.35357e-05 | -3.09817e-05 |
...
Element Axial Forces and Stresses:
|   Element |                N |            Sigma | State       | Phase   |
|         6 | -2.82843e+04     | 2.35702e+06      | Tension     | Elastic |

Assumptions and Notes

• Pin-jointed, small-displacement, linear-elastic truss; no geometric or material nonlinearity.
• Node IDs and element connectivity must be consistent across CSV files.
• Units must be compatible across forces, lengths, and material properties.
• To analyze a new case, edit the three CSV files in io/ and rerun python -m mom_project.main.