BFSC cylinder finite element - bfsccylinder

The bfsccylinder module implements the single-curvature BFSC (SC-BFSC) finite element, a four-node element of the developed mid-surface of a cylindrical shell, for linear and nonlinear analyses, with Donnell-type kinematics, bfsccylinder.bfsccylinder.BFSCCylinder, and Sanders-type kinematics, bfsccylinder.bfsccylinder_sanders.BFSCCylinderSanders. The module gives the elements and the functions that compute the contributions of one element to the matrices and vectors of a model, written in sparse arrays; the model, its boundary conditions and the solution of its equations are written by the user, with NumPy and SciPy. With bfsccylinder you can compute:

• The linear constitutive stiffness matrix \(\boldsymbol{K}_{C0}\), for linear static analyses, \(\boldsymbol{K}_{C0}\boldsymbol{u} = \boldsymbol{F}_{ext}\)

• The geometric stiffness matrix \(\boldsymbol{K}_G\), for linear buckling analyses, \((\boldsymbol{K}_{C0} + \lambda \boldsymbol{K}_G)\boldsymbol{u} = \boldsymbol{0}\), of the membrane stress resultants of a static solution or of a constant membrane stress state

• The mass matrix \(\boldsymbol{M}\), for natural frequency analyses, \((\boldsymbol{K}_{C0} - \omega^2 \boldsymbol{M})\boldsymbol{u} = \boldsymbol{0}\)

• The internal force vector \(\boldsymbol{F}_{int}\) and the tangent stiffness matrix \(\boldsymbol{K}_{C0} + \boldsymbol{K}_{CNL} + \boldsymbol{K}_{GNL} + \boldsymbol{K}_G\), its exact Jacobian, for geometrically nonlinear static analyses

• The force vector and the load stiffness matrix of a follower pressure, normal to the deformed shell

Code repository

saullocastro/bfsccylinder

User guide

• The element and its degrees of freedom
• Donnell-type and Sanders-type kinematics
• Assembling a model
• Analyses
• Follower pressure

Usage examples

• Linear static analysis
• Linear buckling analysis
• Natural frequencies
• Nonlinear static analysis
• Nonlinear static analysis with structsolve
• Follower pressure
• Donnell-type and Sanders-type kinematics

Tutorials

• Tutorials

bfsccylinder API

• API reference
  • Donnell-type cylinder element (bfsccylinder.bfsccylinder)
  • Sanders-type cylinder element (bfsccylinder.bfsccylinder_sanders)
  • Namespace of the Sanders-type element (bfsccylinder.sanders)
  • Gauss-Legendre quadrature (bfsccylinder.quadrature)
  • Utilities (bfsccylinder.utils)

Installing bfsccylinder

• Installing bfsccylinder

Changelog

• Changelog

License

Copyright (c) 2020-2026, Saullo G. P. Castro (S.G.P.Castro@tudelft.nl)
All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Citing this library

Saullo G. P. Castro (2026). Implementation of the BFSC cylinder finite element (Version 0.7.1). saullocastro/bfsccylinder.

In BibTeX:

@misc{castro_bfsccylinder,
  author  = {Castro, Saullo G. P.},
  title   = {Implementation of the BFSC cylinder finite element},
  year    = {2026},
  version = {0.7.1},
  url     = {https://github.com/saullocastro/bfsccylinder}
}

The repository also has a CITATION.cff file with the same data.

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