2D Truss Solver (FEM) using Python

2D truss finite element solver in Python. Assembles the stiffness matrix, solves for displacements, computes stress, strain, axial forces and reactions, and visualizes the deformed structure.

Features

• Sparse stiffness matrix assembly (scipy.sparse)
• Stability check via minimum eigenvalue before solving
• Residual check after solving for numerical quality assurance
• Stress, strain, and axial force per bar
• Deformed shape visualization with coolwarm stress colormap
• Automatic force arrow scaling
• Support symbols (pin, roller-x, roller-y) inferred from boundary conditions
• PlotSettings dataclass for full visualization control

Requirements

• numpy>=1.24
• scipy>=1.10
• matplotlib>=3.7
• Python 3.9+ recommended.

Usage

from truss2d import Nodes, Bars, PlotSettings, solve_truss, plot_truss
import numpy as np

nodes = Nodes(
    coordinates=np.array([
        [0, 4], [3, 4], [0, 0], [3, 0], [6, 0]
    ], dtype=float),
    forces=np.array([
        [0,     0],
        [10000, 0],
        [0,     0],
        [10000, 270],
        [0,     0]
    ], dtype=float),
    boundary_conditions=np.array([0, 1, 4, 8, 9])  # 0-based DOF indices
)

bars = Bars(
    connectivity=np.array([
        [0,1],[0,2],[2,1],[1,3],[1,4],[2,3],[3,4]
    ]),
    E=np.full(7, 2e11),  # Pa
    A=np.full(7, 1e-5)   # m²
)

result = solve_truss(nodes, bars)
result.print_summary(nodes.boundary_conditions)
result.print_summary(nodes.boundary_conditions)

# Default settings
plot_truss(nodes, bars, result)

# Custom settings
plot_truss(nodes, bars, result, PlotSettings(
    scale=10,                  # deformation amplification
    force_scale=None,          # None = auto-scale arrows
    cmap="coolwarm",           # stress colormap
    figsize=(10, 7),
    bar_linewidth=2.5,
    undeformed_alpha=0.3,
    node_color="black",
    node_fontsize=10,
    force_color="green",
    arrow_width=0.009,
    support_symbol_size=0.2,   # tune to match truss scale
))

Force convention

Forces are defined as [magnitude, angle_deg] where 0° points in the +X direction and angles increase counter-clockwise.

Angle	Direction
0°	→ +X
90°	↑ +Y
180°	← -X
270°	↓ -Y

Boundary conditions

boundary_conditions is a list of 0-based DOF indices to constrain:

• Node i has DOFs 2i (x) and 2i+1 (y)
• Constrain both to fix a pin support
• Constrain one to model a roller

Project structure

truss2d/
├── truss2d.py       # solver and visualization
├── example_01.py    # example 01
└── README.md

Output

TrussResult contains:

Field	Description
displacements	Nodal displacement vector (2n,)
stress	Axial stress per bar (m,)
strain	Axial strain per bar (m,)
axial_force	Axial force per bar (m,)
reactions	Full reaction force vector (2n,)