Test Case Results from "A Spline-Based Stress Function Approach for the Principle of Minimum Complementary Energy"

This dataset contains the test case results from the publication "A Spline-Based Stress Function Approach for the Principle of Minimum Complementary Energy".

Context and methodology

The dataset was created within the context of computational mechanics, specifically in the field of solution techniques for elasticity problems. It is associated with the research presented in the publication "A Spline-Based Stress Function Approach for the Principle of Minimum Complementary Energy."

The dataset serves to document the numerical test cases presented in the publication. It provides the stress results obtained through numerical simulations using the proposed spline-based stress function method, supporting comparisons with analytical solutions and the displacement-based finite element method (FEM). These results are used to assess the accuracy and efficiency of the proposed approach.

Technical details

Structure of the dataset

The dataset is organized according to the test cases presented in the publication:

1. Bar under Self-Weight
2. Bending of a Beam by Uniform Transverse Loading
3. Bi-Layer Cantilever with Anisotropic Material Behavior
4. Parabolic-Shaped Cantilever

 Each test case has its own top-level folder. Within each of these folders, there are two subfolders:

• A stress_components folder containing the computed stress results.

• A comparison folder containing data used for comparison with a reference method.

All numerical data is stored in CSV format.

Naming convention

The top-level folder names follow the corresponding test case names.  The file names reflect the data stored (e.g., stress_xx.csv for the xx component of the stress tensor, or stress_components_x_1.5.csv for the comparison of the stress components at x=1.5m).

Additional resources

The dataset additionally includes Python scripts and TikZ .tex files for generating the figures used in the publication, along with the corresponding image files.

Required software

To generate these visualizations, you either need:

• pdfTeX (1.40.27) to compile the provided .tex files using the standalone document class, including the used packages:
  • amsmath (2024-11-01a), pgfplots (1.18.1), siunitx (3.4.6)
• Python  (3.13.5) to run the accompanying plotting scripts, including the used packages:
  • matplotlib (3.10.3), numpy (2.3.1), pandas (2.3.0)

See also the requirements.txt file.

Licenses

• Data is licensed under Creative Commons Attribution 4.0 International.
• Software is licensed under the MIT License.