vereshchaginpy 0.1.4

Graph-based integration for structural mechanics using the Vereshchagin method

VereshchaginPy

VereshchaginPy is a Python library for performing graph multiplication — particularly useful in structural mechanics when applying the flexibility method.

The integration is based on the principle that the integral from two graphs can be expressed as:

∫ Mi(x) * Mj(x) dx = A * y

Where:

• A is the area under the first moment diagram Mi(x)
• y is the corresponding ordinate (value) from the second moment diagram Mj(x) evaluated at the centroid of area A
• Mi, Mj are continuous functions (e.g., moments) over a shared length L

This library helps formalize that process by abstracting common shape-based moment diagrams (rectangles, triangles, trapezoids, parabolas) and automating their integration and visualization.

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Installation

Install the package via pip:

pip install vereshchaginpy

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Example Usage

from vereshchaginpy import Rectangle, TriangleLeft, VereshchaginVisualiser

# Define two figures
r = Rectangle(5, 3)
t = TriangleLeft(5, 2)

# Visualize the interaction
viz = VereshchaginVisualiser()
viz.draw_situation(r, t)

# Compute the integral using the + operator
result = r + t

print(f"Result: {result}")

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Features

• Support for standard structural figure types:
  • Rectangle
  • TriangleLeft, TriangleRight
  • Trapezoid
  • Parabola
  • ParabolicTrapezoid (combining a parabola and trapezoid)
• Clean and extendable figure model
• Visualizer to plot and label diagrams
• Operator overloading for quick integration via +
• Strict input validation for type safety

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Project Links

• GitHub: https://github.com/Haudkozaur/VereshchaginPy
• PyPI: https://pypi.org/project/vereshchaginpy

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License

This project is licensed under the MIT License. See the LICENSE file for details.