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

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, 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.

Instructions for visualization
------------------------------

   1. Stress Components
   For each test case, the "stress_components" folders contain CSV files with the individual components of the stress
   tensor, sampled at specific x- and y-coordinate points. To visualize these stress components, run
   "python3 plot_stress_components.py" from the corresponding subfolder. For convenience, the generated images are also
   included in the dataset.

   2. Comparison
   Each test case additionally includes a "comparison" folder containing the stress data from both the presented method
   and the reference solution. These are provided either as separate or combined CSV files. To generate the
   corresponding plots, a LaTeX file using the standalone document class with TikZ is included in each folder. This
   ".tex" file can be compiled to produce the images used in the publication. To recreate the figures, compile the
   ".tex" file using "pdflatex comparison.tex". Again, the reference images are provided in each subfolder.