EBBEF2p for Python

EBBEF2p (Euler-Bernoulli Beams on Two-Parameter Elastic Foundations) is a finite element package for static analysis of beams on Winkler, Pasternak and modified Vlasov foundations.

• both foundation parameters may vary linearly along the beam, with jumps between segments;
• the soil may continue beyond the beam ends (equivalent end springs);
• modified Vlasov model (Vallabhan & Das, 1991) with iterated decay parameter and depth-dependent soil modulus;
• bending moments and shear forces from element equilibrium;
• soil pressure including the concentrated forces of the shear layer, with a global equilibrium check.

EBBEF2p was originally written as a MATLAB toolbox.

Installation

pip install ebbef2p-python            # NumPy and SciPy only
pip install "ebbef2p-python[plot]"    # with Matplotlib for quick-look plots

Python 3.12 or newer is required.

Quick start

from ebbef2p import Model, solve

model = Model(soil_beyond_ends=True)
model.add_beam(0, 10, E=30e6, I=0.01)
model.add_foundation(0, 10, k=5000, g=2000)   # g = 2t (Vlasov) = Gp (Pasternak)
model.add_point_load(5, force=100)

solution = solve(model, n_elements=100)
print(solution.w.max(), solution.bending_moment().max())
print(solution.equilibrium())

A modified Vlasov foundation is defined by the soil layer instead:

from ebbef2p import Model, VlasovSoil, solve_vlasov

model = Model(soil_beyond_ends=True)
model.add_beam(0, 100, E=432000, I=2.25).add_distributed_load(0, 100, 3)
result = solve_vlasov(model, VlasovSoil(E_top=144, nu=0.2, depth=25))
print(result.gamma, result.k, result.g)

More in the documentation and in the examples folder.

Verification

tests/verification compares EBBEF2p with independent references: closed-form solutions for beams without foundation, Hetényi's long beam on a Winkler foundation, the exact element stiffness and joint rotations of Razaqpur & Shah (1991), the decay parameter gamma of Vallabhan & Das (1991), numerical integration of the element matrices and Vlasov parameters, and global equilibrium. The full table is in the documentation.

Development

The project uses uv:

uv sync          # environment with the package and the dev tools
uv run pytest    # tests/unit and tests/verification
uv run ruff check .

See CONTRIBUTING.md for guidelines and CHANGELOG.md for the changes since 0.0.x, including how to migrate from the old Structure API.

Citing

If you use EBBEF2p in your work, please cite it using the metadata in CITATION.cff (GitHub shows it under Cite this repository). The software is archived on Zenodo: 10.5281/zenodo.23665165 (all versions; each release also has its own DOI).

License

MIT, see LICENSE.