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milcapy

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milcapy

Python library for 2D structural analysis of frames, trusses, and finite element membranes

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What is milcapy?

milcapy is a comprehensive Python library for structural analysis of 2D frames and finite element membranes. It implements the direct stiffness method for frames and trusses, and the finite element method for membrane analysis, with closed-form solutions for 1D elements. The library incorporates advanced concepts from matrix structural analysis and supports multiple beam theories and membrane element types.

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Key Features

Frame & Truss Analysis

Analyze 2D frames and trusses with Timoshenko and Euler-Bernoulli beam theories

Finite Element Membranes

Multiple membrane elements: CST, Q4, Q6, Q6i, and Q8 with plane stress/strain

Advanced Features

End offsets (rigid arms), releases, elastic supports, and local node axes

Interactive Visualization

Built-in model viewer with deformation plots, force diagrams, and results

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Supported Elements

milcapy supports a comprehensive range of structural elements:

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1D Elements

  • Beams: Timoshenko and Euler-Bernoulli beam theories
  • Trusses: Axial force members

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2D Membrane Elements

  • CST: Constant Strain Triangle (3 nodes, 2 DOF per node)
  • Q4: Quadrilateral with 4 nodes and 2 DOF per node
  • Q6: Quadrilateral with 4 nodes and 3 DOF per node (includes drilling DOF)
  • Q6i: Rectangular element with 4 nodes, 2 DOF per node, and incompatible modes
  • Q8: Quadrilateral with 8 nodes (4 mid-side nodes condensed), 2 DOF per node

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Element Convergence

The library includes highly accurate finite element formulations. Below is a convergence study for a cantilever beam (2m length, 0.6m × 0.4m cross-section, E=2×10⁶, ν=0.2, 20 tonf tip load): Element convergence study
The Q8 element shows excellent convergence with a single element, while Q4 requires mesh refinement for accurate results.

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Quick Example

from milcapy import SystemModel, BeamTheoriesType

# Create model
model = SystemModel()

# Define material and section
model.add_material("concrete", modulus_elasticity=2.1e6, poisson_ratio=0.2)
model.add_rectangular_section("beam", "concrete", base=0.3, height=0.5)

# Add nodes
model.add_node(1, 0, 0)
model.add_node(2, 5, 0)

# Add member
model.add_member(1, 1, 2, "beam", BeamTheoriesType.TIMOSHENKO)

# Apply boundary conditions
model.add_restraint(1, True, True, True)
model.add_restraint(2, False, True, False)

# Add loads
model.add_load_pattern("Live Load")
model.add_point_load(2, "Live Load", fx=0, fy=-100, mz=0)

# Solve
model.solve()

# Get results
results = model.get_results("Live Load")
displacements = results.get_node_displacements(2)
print(f"Node 2 displacement: {displacements}")

# Visualize
model.show()

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Installation

Install milcapy using pip: 
pip install milcapy

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Requirements

  • Python ≥ 3.10
  • NumPy
  • Matplotlib

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Next Steps

Installation

Get milcapy installed on your system

Quickstart

Build your first structural model

Core Concepts

Learn the fundamental concepts

API Reference

Explore the complete API

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About

milcapy is developed by Amilcar Machacca Mayo.

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