libThinPlateShells

This code repo implements the techniques presented in the Eurographics 2025 conference paper: Corotational Hinge-based Thin Plates/Shells.

Bending Models for the Thin Shell

Corotational hinge-based thin plates/shells

• We present a corotational edge-based hinge curvature operator for thin shell simulation, including a specific variant for thin plate simulation. (EP/ES --- edge-based hinge thin plate/shell model)
• We propose a corotational FVM (finite volume method) hinge curvature operator for thin shell simulation, along with a specific variant for thin plate simulation. (FS/FP --- FVM hinge thin plate/shell model)
• We introduce a corotational smoothed hinge curvature operator for thin shell simulation, as well as a specific variant for thin plate simulation. (SS/SP --- smoothed hinge thin plate/shell model)
• All six thin plate/shell models feature constant bending energy Hessians, with detailed boundary conditions for accurate simulation.

Quadratic and Cubic Shells

We aim to improve the accuracy of the Quadratic Shell (QS), and the Cubic Shell model (CS) by identifying the rational bending rigidity for edge-based hinge bending models.

The corresponding Quadratic Thin Plate/Shell (QTP/QTS) formulations with the rational bending rigidity are provide in the Appendix of our paper. QTP/QTS also can be seen as a specific variant of EP/ES.

Thin shells using midedge operators

The midedge operators are adapted from the libshell library, which includes three types of formulations: MidedgeAve, MidedgeTan, MidedgeSin, for comparison. (MidEdgeAve/Tan/Sin)

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13 different bending formulations are included in this repo. These formulations are labeled as: EP, ES, FP, FS, SP, SS, QS, CS, QTP, QTS, MidEdgeAve, MidEdgeSin, MidEdgeTan.

Benchmark Cases

We provide the tested benchmark data in the data folder. For the geometrically non-linear shell benchmarks, the ABAQUS .inp files are also provided.

Linear plate bending benchmark.

• A square plate with simply supported boundaries, subjected to a uniform load perpendicular to its plane.

Geometrically non-linear shell benchmarks.

• Cantilever plate subjected to end shear force.
• Hemispherical shell subjected to alternating radial forces.

Data Structure and Parallelization

The data structure of this repository is inspired by libshell and WrinkledTensionFields. The code has been parallelized using the Threading Building Blocks (TBB) library to enhance performance.

Dependencies

• Libigl
• Polyscope
• TBB
• Json
• Suite Sparse

Build

The code has been tested only on Linux.

Install SuiteSparse

sudo apt-get update -y
sudo apt-get install -y libsuitesparse-dev

Clone and Build the Project

Use the following commands to download and compile the project:

    git clone https://github.com/liangqx-hku/libThinPlateShells.git
    cd LibThinShells
    mkdir build
    cd build
    cmake ..
    make

Run the Project

You can execute the program with the following command:

sh runCmd.sh

Customize Input and Output

In the runCmd.sh, you can specify the paths for the input JSON file and the output mesh file:

./bin/ThinShellCli_bin -i ../data/elastic/slit_plate/slit_plate.json -o ../data/elastic/slit_plate/output/output_slit_plate51.obj

Configuration Parameters

The following parameters in the JSON file should be specified, others are default for thin shell tests in this project.

• bending_type: Specifies the bending model. Options include EP, ES, FP, FS, SP, SS for our proposed models. QS/CS specify Quadratic/Cubic Shlls.

  • For midedge formulations, use midEdgeShell with sff_type to specify the discrete second fundamental form:
    • midedgeAve (default)
    • midedgeTan
    • midedgeSin
  • When using EP, ES, FP, FS, SP, SS, sff_type must be set to midedgeAve for data structure consistency.
  • (Note: QTP/QTS are implemented within EP/ES but are not provided for direct execution.)

• clamped_DOFs: Path to the .dat file containing clamped degrees of freedom, formatted as (DOF index, coordinate at the clamped dof).

• curedge_DOFs: Specifies midedge rotation degrees of freedom for midedge formulations.

• rest_mesh: Path to the .obj file for the initial configuration.

• output_mesh: Path to the .obj file for the final configuration.

• point_Forces: Path to the .dat file storing all point forces, formatted as (DOF index, force value).

• gravity: Gravity force magnitude in the X, Y, and Z directions.

• density: Material density.

• poisson_ratio: Poisson’s ratio.

• thickness: Shell thickness.

• youngs_modulus: Young’s modulus.

• stretching_type: Specifies the material model (StVK is used in this project).

• rest_flat: A flag indicating whether the initial mesh is flat (zero second fundamental form) for midedge formulations.

GUI with Polyscope

We also provide a GUI version of the executable program: ThinShellGui_bin. The input parameters for the GUI version are identical to those used in the command-line counterpart.

Contact

If you have any question, please feel free to contact me at liangqixin23@outlook.com