This project is an independent exploration of computational structural analysis using MATLAB. It analyzes a two-dimensional pin-jointed truss with the direct stiffness method, then evaluates member forces, stresses, factors of safety, deformation, and structural mass.
The project extends my progression from projectile motion and beam mechanics into statics, matrix structural analysis, and engineering design optimization.
- 2D truss node and member definitions
- Pinned and roller support constraints
- Global stiffness-matrix assembly
- Nodal displacement solution
- Support reaction recovery
- Member tension and compression forces
- Axial stress and factor-of-safety evaluation
- Structural mass estimation
- Exaggerated deformed-shape visualization
- Load sensitivity and cross-sectional-area experiments
- Minimum-mass grid search subject to FOS and deflection limits
The included example is a triangular truss with nodes (0, 0), (2, 0), and (1, 1.5) m. Node 1 is pinned, node 2 is a vertical roller, and a downward load is applied at node 3.
| Parameter | Reference value |
|---|---|
| Young's modulus | 200 GPa |
| Yield strength | 250 MPa |
| Density | 7850 kg/m³ |
| Uniform member area | 100 mm² |
| Downward load | 1000 N |
- Open MATLAB.
- Set the current folder to the repository root.
- Run
src/main.m. - Press Enter at prompts to use the reference defaults.
- Review the printed results, member states, deformed-shape plot, and lightweight design search.
The code uses the direct stiffness equation:
[ [K]{u} = {F} ]
See docs/theory.md for the derivation, sign conventions, and limitations.
matlab-truss-analysis-optimization/
├── README.md
├── LICENSE
├── src/
│ ├── main.m
│ ├── define_nodes.m
│ ├── define_members.m
│ ├── define_loads.m
│ ├── define_supports.m
│ ├── element_stiffness.m
│ ├── assemble_global_matrix.m
│ ├── solve_displacements.m
│ ├── calculate_member_results.m
│ └── analyze_truss.m
├── optimization/
│ └── optimize_truss.m
├── examples/
│ └── simple_truss.m
├── results/
│ ├── truss_response.png
│ ├── stress_map.png
│ ├── load_sensitivity.png
│ ├── area_tradeoff.png
│ └── optimization.png
├── docs/
│ └── theory.md
└── scripts/
├── generate_results.py
└── test_model.py
The gray dashed geometry is the original truss. The colored geometry is the deformed truss with deformation magnified for visibility; it is explicitly not to scale. Blue members are in tension and red members are in compression.
The load experiment tests 500, 1000, 1500, 2000, and 2500 N. In the linear-elastic model, displacement and stress increase proportionally with load.
The area experiment tests uniform member areas of 50, 75, 100, 150, and 200 mm². Larger areas reduce stress and deflection while increasing structural mass.
The optimization search tests areas from 10 to 300 mm² and selects the lightest uniform area satisfying FOS ≥ 2.0 and maximum displacement ≤ 5 mm for the reference load case.
This project helped me connect static equilibrium, axial member behavior, matrix assembly, boundary conditions, linear-system solving, stress evaluation, and constrained engineering design. It also made the relationship between material area, structural weight, and performance visible through parameter studies.
This is an educational linear-elastic truss solver. It does not include buckling, member bending, joint slip, self-weight, multiple load cases, or 3D geometry. Future improvements could add distributed load conversion, multiple point loads, additional truss topologies, cross-section selection, MATLAB App Designer controls, and comparison with a commercial finite-element tool.
This project is licensed under the MIT License. See LICENSE.