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Semi-analytical methods for plates, shells and stiffened panels

• Linear and non-linear static analyses, with field outputs of displacements, strains and stresses
• Linear buckling
• Vibration, with or without pre-stress
• Panel flutter using the piston theory
• Geometrically non-linear static analyses (postbuckling) using the Newton-Raphson method or the arc-length methods of Riks and Crisfield
• Dead or follower (hydrostatic) pressure loads, with the unsymmetric load stiffness of the follower pressure
• Multi-domain assemblies of plates, cylindrical shells, cylinders, stiffened panels, with the domains connected exactly with the null-space method, the default, or by penalty stiffnesses. Debonding defects or cohesive zone can be simulated
• CLPT, FSDT and TSDT kinematics for plates and cylindrical shells
• Donnell and Sanders-Koiter kinematics for cylindrical shells

The structural matrices are solved with structsolve.

Citing this library

Saullo G. P. Castro, Nathan D'Souza. (2026). Semi-analytical methods for plates, shells and stiffened panels (Version 0.11.0). Zenodo. DOI: https://doi.org/10.5281/zenodo.2541522.

Documentation

The documentation is available on: https://saullocastro.github.io/panels.

Installation

To get the latest version:

python -m pip install panels

History

See CHANGELOG.md for the details of each version.

• version 0.11.0 (2026-10-07)
  • Follower (hydrostatic) pressure loads, Shell.add_pressure_load(..., follower=True), with the unsymmetric load stiffness kCfollower in Shell and MultiDomain
  • Theory documentation, verification tests and validation notebooks of the follower pressure
  • Interactive 3D plots of multi-domain assemblies with plotly, MultiDomain.plot3d()
  • Improved Cython and compiler flags
  • TSDT uses Laminate.Dts and Laminate.Fts, requires composites>=0.9.12 and structsolve>=0.5.0
• version 0.9.0 (2026-09-24)
  • Null-space connection, exact, new default, as alternative to penalty-based connection
• version 0.8.0 (2026-09-23)
  • FSDT and TSDT for plate and cylindrical shells
  • Sanders-Koiter for cylindrical shells
  • Shell and Multidomain connections supporting FSDT, TSDT and Sanders-Koiter kinematics
  • Many improvements in the documentation
  • New tests based on literature
  • BUG fixes on aerodynamic matrix of cylindrical shells and mass matrix of stiffener 1D
• version 0.7.1 (2026-09-21)
  • Fixed the cohesive zone of the MultiDomain connection 'SB_TSL', which could not capture the onset of failure of the DCB: tangential separation with the rotation of each panel, tractions with the uncorrected separation and separation correction as in the thesis of D'Souza (2024)
  • Consistent tangent of the cohesive zone, MultiDomain.calc_kT_TSL(), and faster assembly of the 'SB_TSL' secant stiffness
  • The kernels fkCSB11_dmg, fkCSB12_dmg and fkCSB22_dmg take the distances dt and db from each mid-surface to the interface
  • Validation of the cohesive zone against mode I DCB results in the literature, in notebooks/, with a convergence study
  • Fixed StiffPanelBay.save() with composites>=0.9.0
• version 0.6.21 (2026-09-18)
  • Fixed the mass of the base of BladeStiff2D, which was missing, and the section forces of MultiDomain.force(), which lacked the Jacobian
  • StiffPanelBay.calc_kA() sums the contribution of every panel, and calc_kA, calc_cA, calc_fext, save, get_size and uvw_stiffener of StiffPanelBay and Shell.calc_cA no longer raise
  • Shell.strain() and Shell.stress() work for a plate with r=None
  • Line coverage of the tests raised from 67 % to 92 %
  • Fixed StiffPanelBay.add_panel and the partial-domain integration of Shell.calc_kC, calc_kG and calc_kM
  • The limits Shell.x1, x2, y1, y2 of the integration domain default to None instead of the sentinels -1 and +1, which silently integrated the full domain for a limit at 1.0 and ignored a limit given on one side only; the old -1 now raises
  • Fixed the MultiDomain skin-base connections: the 'SB' penalty was a hard-coded mm-unit value, the top and bottom panels depended on their order in the assembly, and the connection dictionaries were modified
  • Penalty constants of each MultiDomain connection can be given with 'kt' and 'kr'
  • Reproduction of Stamatelos and Labeas with plate domains only in tests/multidomain/test_stamatelos_labeas_2023_multidomain.py, using every MultiDomain connection
  • Fixed the argument handling of the stiffness API: an invalid c or c_cte no longer reaches the nogil kernels, and a model that needs a radius raises instead of computing with r = 0
  • Reproduction of Stamatelos and Labeas (Computation 2023, 11, 110) in notebooks/stamatelos_labeas_2023.ipynb
  • Tangent stiffness matrix that is the exact derivative of the internal force vector, giving quadratic convergence to the Newton-Raphson method
  • Shell and MultiDomain can be passed directly to structsolve.Analysis, including the arc-length methods
  • Gauss-Legendre points and weights from scipy.special.roots_legendre
  • Modules of the models renamed without the _bardell suffix, and the legacy _bardell model names removed from panels.modelDB.db
  • Sphinx documentation with usage examples
• versions 0.5.x
  • Damaged multidomain connections
• up to version 0.3.x
  • Multidomain methods for pristine structures

License

Distributed under the 3-Clause BSD license (https://raw.github.com/saullocastro/panels/main/LICENSE).

Contact: S.G.P.Castro@tudelft.nl