3pc-lambuck

3pc-lambuck is a Python library for buckling analysis of shear deformable anisotropic laminates and sandwich plates. It provides a Lambuck class to solve the generalized eigenvalue problem to calculate critical buckling loads and mode shapes based on first-order shear deformation theory (FSDT) and classical laminate theory (CLT).

Installation

Use the package manager pip to install 3pc-lambuck. Since the package and its dependencies are available on PyPI, you can install them directly:

pip install 3pc-lambuck

API Reference

Lambuck Class

The primary component of this package is the Lambuck class, which takes a panel and a load case to compute buckling metrics.

from lambuck.lambuck import Lambuck

Required Parameters

When initializing Lambuck, the following parameters are required:

• panel (Panel): An instance of the Panel class (from 3pc-panel) containing the laminate definition and geometry.
• loads (Loads): An instance of the Loads class (from 3pc-loads) containing the load case and environmental conditions.
• number_of_terms (int): Number of terms to include in the Ritz/Fourier series expansion.
• number_of_points_x (int): Number of evaluation points along the x-axis.
• number_of_points_y (int): Number of evaluation points along the y-axis.

Calculated Properties

The class calculates the following properties:

• NT, NC: Thermal and hygral in-plane load vectors.
• pairs: List of $(m, n)$ pairs for Ritz terms.
• K33: Part of stiffness matrix dependent on tensile loads.
• F33: Matrix representing load-dependent contribution.
• lambdaEV: Eigenvalues of the generalized eigenvalue problem $K = \lambda F_{33}$.
• vr: Right eigenvectors.
• lambda_cr: Critical eigenvalue (same as lambda1).
• vr_cr: Critical right eigenvector.
• mn_cr: Critical $(m, n)$ pair.
• lambdaP: Sorted list of positive eigenvalues.
• lambda1, lambda2, lambda3, lambda4, lambda5: The first five critical (lowest positive) eigenvalues.
• mn1, mn2, mn3, mn4, mn5: Dominant $(m, n)$ pairs for the first five eigenvalues.
• Nxxcr1, Nyycr1, Nxycr1 to Nxxcr5, Nyycr5, Nxycr5: Critical buckling loads (for modes 1 to 5).

Methods

Lambuck.fromDict(**kwargs)

Initializes a Lambuck instance using a dictionary of keyword arguments.

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Usage Examples

Basic Initialization

Below is an example of performing a buckling analysis on a panel under a specific load case.

from panel.panel import Panel
from loads.loads import Loads
from lambuck.lambuck import Lambuck

# Assuming pnl (Panel) and ld (Loads) are already defined
s001 = Lambuck(
    panel=pnl,
    loads=ld,
    number_of_terms=8,
    number_of_points_x=5,
    number_of_points_y=5
)

# Access critical buckling load and eigenvalue
print("Critical Eigenvalue:", s001.lambda_cr)
print("First critical eigenvalues (modes 1-5):", s001.lambda1, s001.lambda2, s001.lambda3, s001.lambda4, s001.lambda5)

Commands

The package provides a command-line interface entry point. After installing, you can run the application using:

lambuck input.cfg

(This entry point is defined in lambuck.__main__:main)

Options

• config (positional): Specify the configuration file (.cfg) to run the analysis.
• -h, --help: Show the help message and exit.
• -v, --version: Show the version number.
• -s, --sample: Copy example files (materials, plies, laminates, etc.) to the current directory.

Configuration File (lambuck.cfg)

The lambuck command requires a configuration file (typically named lambuck.cfg). Below is an example based on lambuck/examples/composite006/lambuck.cfg:

[files]
materials = materials.json
plies = plies.json
laminates = laminates.json
panels = panels.json
loads = loads.json
output = output.txt

[analysis]
number_of_terms = 8
number_of_points_x = 5
number_of_points_y = 5

[files] Section

This section defines the paths to the required input JSON files and the desired output file:

• materials: Path to the materials JSON file. Follows the format expected by 3pc-material.
• plies: Path to the plies JSON file. Follows the format expected by 3pc-ply.
• laminates: Path to the laminates JSON file. Follows the format expected by 3pc-laminate.
• panels: Path to the panels JSON file. Follows the format expected by 3pc-panel.
• loads: Path to the loads JSON file. Follows the format expected by 3pc-loads.
• output: Path to the text file where the buckling analysis results will be written.

[analysis] Section

This section specifies the analysis settings:

• number_of_terms: Number of terms to include in the Ritz/Fourier series.
• number_of_points_x: Number of evaluation points along the x-axis.
• number_of_points_y: Number of evaluation points along the y-axis.

Citation

If you use this library in your research or work, please cite it as follows:

APA Format:

Rastogi, N., & Seresta, O. (2026). 3pc-lambuck: Python library for buckling analysis of shear deformable anisotropic laminates and sandwich plates. PyPI. https://pypi.org/project/3pc-lambuck/

BibTeX:

@software{3pc_lambuck,
  author = {Rastogi, Naveen and Seresta, Omprakash},
  title = {3pc-lambuck: Python library for buckling analysis of shear deformable anisotropic laminates and sandwich plates},
  year = {2026},
  url = {https://pypi.org/project/3pc-lambuck/}
}