Semi-analytical methods for plates, shells and stiffened panels - panels#
The panels module provides semi-analytical (Ritz) models for plates,
cylindrical shells and stiffened panels, using
Bardell’s hierarchical functions as approximation
functions. The structural matrices and force vectors are solved with
structsolve. With panels
you can run:
Linear static analyses, with field outputs of displacements, strains and stresses
Linear buckling analyses, with the pre-buckling stress state given by constant stress resultants or calculated with a static analysis
Frequency analyses, with or without pre-stress
Panel flutter analyses, using the piston theory
Geometrically non-linear static analyses based on Donnell’s equations, with a tangent stiffness matrix that is the exact derivative of the internal force vector, using:
the Newton-Raphson method
the arc-length methods of Riks and Crisfield, able to trace limit points and snap-through
Multi-domain analyses, connecting shell domains exactly with the null-space method, the default, or with penalty stiffnesses, to model cylinders, stiffened panels and panels with debonding defects, also with the shear deformation theories
The models are identified by the type of structure, the kinematic theory and
the non-linear equations, see panels.models:
'plate_clpt_donnell': plates, classical laminated plate theory (CLPT)'plate_fsdt_donnell': plates, first-order shear deformation theory'plate_tsdt_donnell': plates, third-order shear deformation theory of Reddy'cylshell_clpt_donnell': cylindrical shells, CLPT with Donnell’s kinematics'cylshell_clpt_sanders': cylindrical shells, CLPT with Sanders-Koiter’s kinematics, which give zero strains for rigid-body motions'cylshell_fsdt_donnell','cylshell_tsdt_donnell': cylindrical shells, first-order and third-order shear deformation theories with Donnell’s kinematics'cylshell_fsdt_sanders','cylshell_tsdt_sanders': cylindrical shells, first-order and third-order shear deformation theories with Sanders-Koiter’s kinematics
Code repository#
Citing this library#
Saullo G. P. Castro, Nathan D’Souza. (2026). Semi-analytical methods for plates, shells and stiffened panels (Version 0.9.0). Zenodo. DOI: https://doi.org/10.5281/zenodo.2541522.
Usage examples#
- Linear static analysis
- Linear buckling analysis
- Frequency analysis
- Panel flutter analysis
- Non-linear static analysis with the Newton-Raphson method
- Non-linear static analysis with the arc-length methods
- Cylinders modeled as multi-domain assemblies
- Panels with a T-stiffener modeled as multi-domain assemblies
panels API#
- API reference
- Semi-analytical models for plates, shells and panels (
panels) - Plates and cylindrical shells (
panels.shell) - External force vector (
panels.shell_fext) - Contour plots (
panels.plot_shell) - Model database (
panels.modelDB) - Multi-domain assemblies (
panels.multidomain) - Cylinders modeled as multi-domain assemblies
- Panels with a T-stiffener modeled as 2D domains
- Blade stiffeners (
panels.stiffener) - Stiffened panel bays (
panels.stiffpanelbay)
- Semi-analytical models for plates, shells and panels (
Theory#
Installing panels#
Install from the distributed packages by simply doing:
python -m pip install panels
or from the source code, which requires a C++ compiler to build the Cython extensions, using:
python -m pip install .
Changelog#
License#
Copyright (c) 2012-2026, Saullo G. P. Castro (S.G.P.Castro@tudelft.nl), Nathan D'Souza.
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.