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Graph-based integration for structural mechanics using the Vereshchagin method
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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.
Install the package via pip:
pip install vereshchaginpy
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}")
Rectangle
TriangleLeft
, TriangleRight
Trapezoid
Parabola
ParabolicTrapezoid
(combining a parabola and trapezoid)+
This project is licensed under the MIT License. See the LICENSE
file for details.
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Graph-based integration for structural mechanics using the Vereshchagin method
We found that vereshchaginpy demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 1 open source maintainer collaborating on the project.
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