# PyTopo3D: 3D SIMP Topology Optimization Framework for Python
A comprehensive Python implementation of 3D Topology Optimization based on SIMP (Solid Isotropic Material with Penalization) method. Unlike traditional MATLAB implementations, PyTopo3D brings the power of 3D SIMP-based optimization to the Python ecosystem with support for obstacle regions.
## Table of Contents
- [PyTopo3D: 3D SIMP Topology Optimization Framework for Python](#pytopo3d-3d-simp-topology-optimization-framework-for-python)
- [Table of Contents](#table-of-contents)
- [Overview](#overview)
- [Installation](#installation)
- [Basic Usage](#basic-usage)
- [Configuration Parameters](#configuration-parameters)
- [Command-line Interface](#command-line-interface)
- [Python Package API](#python-package-api)
- [Advanced Features](#advanced-features)
- [Obstacle Configuration](#obstacle-configuration)
- [Command Line Usage](#command-line-usage)
- [Python API Usage](#python-api-usage)
- [Obstacle Configuration Format](#obstacle-configuration-format)
- [Design Space Customization](#design-space-customization)
- [Command Line Usage](#command-line-usage-1)
- [Python API Usage](#python-api-usage-1)
- [Understanding Pitch and Resolution](#understanding-pitch-and-resolution)
- [Exporting Results](#exporting-results)
- [Command Line Usage](#command-line-usage-2)
- [Animation Generation](#animation-generation)
- [Experiment Management](#experiment-management)
- [Command Line Options](#command-line-options)
- [Acknowledgements](#acknowledgements)
- [Citation](#citation)
## Overview
This code performs 3D structural topology optimization using the SIMP (Solid Isotropic Material with Penalization) method. It is designed to be efficient by utilizing:
- Parallel solver (PyPardiso if available, otherwise SciPy's spsolve)
- Precomputed assembly mapping for fast matrix assembly
- Support for obstacle regions where no material can be placed
- Flexible obstacle configuration via JSON files
- Advanced visualization capabilities including animation generation
## Installation
1. Clone this repository:
```bash
git clone https://github.com/jihoonkim888/PyTopo3D.git
cd PyTopo3D
```
2. Create and activate the conda environment:
```bash
# Create the environment from the environment.yml file
conda env create -f environment.yml
# Activate the environment
conda activate pytopo3d
```
## Basic Usage
### Configuration Parameters
The main optimization parameters are:
- `nelx`, `nely`, `nelz`: Number of elements in x, y, z directions (default: 60, 30, 20)
- `volfrac`: Volume fraction constraint (0.0-1.0) (default: 0.3)
- `penal`: Penalization power for SIMP method (default: 3.0)
- `rmin`: Filter radius for sensitivity filtering (default: 3.0)
- `disp_thres`: Display threshold for 3D visualization (elements with density > disp_thres are shown) (default: 0.5)
- `tolx`: Convergence tolerance on design change (default: 0.01)
- `maxloop`: Maximum number of iterations (default: 2000)
### Command-line Interface
To run a basic optimization:
```bash
python main.py --nelx 32 --nely 16 --nelz 16 --volfrac 0.3 --penal 3.0 --rmin 3.0
```
For full options:
```bash
python main.py --help
```
### Python Package API
```python
import numpy as np
from pytopo3d.core.optimizer import top3d
# Define parameters
nelx, nely, nelz = 32, 16, 16
volfrac = 0.3
penal = 3.0
rmin = 3.0
disp_thres = 0.5
# Run optimization
result = top3d(nelx, nely, nelz, volfrac, penal, rmin, disp_thres)
# Save result
np.save("optimized_design.npy", result)
```
## Advanced Features
### Obstacle Configuration
PyTopo3D supports defining regions where material should not be placed during optimization.
#### Command Line Usage
```bash
python main.py --obstacle-config examples/obstacles_config_cylinder.json
```
#### Python API Usage
```python
# Create a custom obstacle mask
obstacle_mask = np.zeros((nely, nelx, nelz), dtype=bool)
obstacle_mask[5:15, 3:7, 3:7] = True # Example obstacle
# Or load obstacles from config file
from pytopo3d.preprocessing.geometry import load_geometry_data
design_space_mask, obstacle_mask, combined_obstacle_mask = load_geometry_data(
nelx=nelx,
nely=nely,
nelz=nelz,
obstacle_config="path/to/config.json"
)
# Use the mask in optimization
result = top3d(nelx, nely, nelz, volfrac, penal, rmin, disp_thres,
obstacle_mask=combined_obstacle_mask)
```
#### Obstacle Configuration Format
The obstacle configuration file is a JSON file with the following structure:
```json
{
"obstacles": [
{
"type": "cube",
"center": [0.5, 0.5, 0.2], // x, y, z as fractions [0-1]
"size": 0.15 // single value for a cube
},
{
"type": "sphere",
"center": [0.25, 0.25, 0.6],
"radius": 0.1
},
{
"type": "cylinder",
"center": [0.75, 0.5, 0.5],
"radius": 0.08,
"height": 0.7,
"axis": 2 // 0=x, 1=y, 2=z
},
{
"type": "cube",
"center": [0.25, 0.75, 0.5],
"size": [0.15, 0.05, 0.3] // [x, y, z] for a cuboid
}
]
}
```
Supported obstacle types:
- `cube`: A cube or cuboid. Use `size` as a single value for a cube, or as `[x, y, z]` for a cuboid.
- `sphere`: A sphere. Use `radius` to set the size.
- `cylinder`: A cylinder. Use `radius`, `height`, and `axis` (0=x, 1=y, 2=z) to configure.
All positions are specified as fractions [0-1] of the domain size, making it easy to reuse configurations across different mesh resolutions.
### Design Space Customization
PyTopo3D allows using STL files to define the design space geometry, enabling complex shapes beyond the standard rectangular domain.
#### Command Line Usage
```bash
python main.py --design-space-stl path/to/design_space.stl --pitch 0.5
```
Command line options:
- `--design-space-stl`: Path to an STL file defining the design space geometry
- `--pitch`: Distance between voxel centers when voxelizing STL (default: 1.0, smaller values create finer detail)
- `--invert-design-space`: Flag to invert the design space (treat STL as void space rather than design space)
#### Python API Usage
```python
from pytopo3d.preprocessing.geometry import load_geometry_data
import numpy as np
# Load design space from STL
design_space_mask, obstacle_mask, combined_obstacle_mask = load_geometry_data(
nelx=60,
nely=30,
nelz=20,
design_space_stl="path/to/design_space.stl",
pitch=0.5,
invert_design_space=False
)
# The shape of the mask is determined by the STL geometry and pitch
nely, nelx, nelz = design_space_mask.shape
print(f"Resolution from voxelization: {nely}x{nelx}x{nelz}")
# Use the mask in optimization
from pytopo3d.core.optimizer import top3d
result = top3d(
nelx=nelx,
nely=nely,
nelz=nelz,
volfrac=0.3,
penal=3.0,
rmin=3.0,
disp_thres=0.5,
obstacle_mask=combined_obstacle_mask
)
```
#### Understanding Pitch and Resolution
The `pitch` parameter directly controls the resolution of the voxelized model:
- Smaller pitch values create higher resolution voxelizations
- The number of voxels along any dimension = physical length รท pitch
- Choose pitch value based on the level of detail needed and computational resources available
### Exporting Results
You can export the final optimization result as an STL file for 3D printing or further analysis in CAD software.
#### Command Line Usage
```bash
python main.py --nelx 32 --nely 16 --nelz 16 \
--volfrac 0.3 --penal 3.0 --rmin 3.0 \
--export-stl \
[--stl-level 0.5] \
[--smooth-stl] \
[--smooth-iterations 5]
```
Options:
- `--export-stl`: Flag to enable STL export of the final optimization result
- `--stl-level`: Contour level for the marching cubes algorithm (default: 0.5)
- `--smooth-stl`: Flag to apply Laplacian smoothing to the mesh (default: True)
- `--smooth-iterations`: Number of iterations for mesh smoothing (default: 5)
### Animation Generation
PyTopo3D can generate animations of the optimization process.
```bash
python main.py --nelx 32 --nely 16 --nelz 16 \
--create-animation \
--animation-frequency 10 \
--animation-frames 50 \
--animation-fps 5
```
Options:
- `--create-animation`: Flag to enable animation generation
- `--animation-frequency`: Store every N iterations for the animation (default: 10)
- `--animation-frames`: Target number of frames in the final animation (default: 50)
- `--animation-fps`: Frames per second in the generated animation (default: 5)
### Experiment Management
PyTopo3D includes a robust experiment management system that automatically:
- Creates a uniquely named directory for each optimization run
- Saves all relevant parameters, inputs, and outputs
- Generates detailed logs of the optimization process
- Records performance metrics and convergence data
#### Command Line Options
```bash
python main.py --experiment-name custom_name \
--description "Detailed description of this experiment" \
--log-level DEBUG \
--log-file custom_log.log \
--verbose
```
Options:
- `--experiment-name`: Custom name for the experiment (optional, auto-generated if not provided)
- `--description`: Description of the experiment stored in the results metadata
- `--log-level`: Set logging detail level (DEBUG, INFO, WARNING, ERROR, CRITICAL)
- `--log-file`: Path to a custom log file
- `--verbose`: Enable more detailed output (sets log level to DEBUG)
- `--quiet`: Reduce output verbosity (sets log level to WARNING)
## Acknowledgements
This code is adapted from [Liu & Tovar's MATLAB code](https://www.top3d.app/) for 3D topology optimization.
> K. Liu and A. Tovar, "An efficient 3D topology optimization code written in Matlab", Struct Multidisc Optim, 50(6): 1175-1196, 2014, doi:10.1007/s00158-014-1107-x
## Citation
If you use PyTopo3D in your research or work, please cite our paper on ArXiv: [PyTopo3D: A Python Framework for 3D SIMP-based Topology Optimization](https://arxiv.org/abs/2504.05604)
> Kim, J. & Kang, N. (2024). PyTopo3D: A Python Framework for 3D SIMP-based Topology Optimization. arXiv preprint arXiv:2504.05604.
```bibtex
@article{kim2025pytopo3d
title={PyTopo3D: A Python Framework for 3D SIMP-based Topology Optimization},
author={Jihoon Kim and Namwoo Kang},
journal={arXiv preprint arXiv:2504.05604},
year={2025}
}
```
This paper provides a detailed explanation of the implementation, theoretical foundations, and optimizations used in PyTopo3D. Proper citation helps support the continued development of open-source scientific software.
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"description": "# PyTopo3D: 3D SIMP Topology Optimization Framework for Python\r\n\r\n\r\n\r\nA comprehensive Python implementation of 3D Topology Optimization based on SIMP (Solid Isotropic Material with Penalization) method. Unlike traditional MATLAB implementations, PyTopo3D brings the power of 3D SIMP-based optimization to the Python ecosystem with support for obstacle regions.\r\n\r\n## Table of Contents\r\n- [PyTopo3D: 3D SIMP Topology Optimization Framework for Python](#pytopo3d-3d-simp-topology-optimization-framework-for-python)\r\n - [Table of Contents](#table-of-contents)\r\n - [Overview](#overview)\r\n - [Installation](#installation)\r\n - [Basic Usage](#basic-usage)\r\n - [Configuration Parameters](#configuration-parameters)\r\n - [Command-line Interface](#command-line-interface)\r\n - [Python Package API](#python-package-api)\r\n - [Advanced Features](#advanced-features)\r\n - [Obstacle Configuration](#obstacle-configuration)\r\n - [Command Line Usage](#command-line-usage)\r\n - [Python API Usage](#python-api-usage)\r\n - [Obstacle Configuration Format](#obstacle-configuration-format)\r\n - [Design Space Customization](#design-space-customization)\r\n - [Command Line Usage](#command-line-usage-1)\r\n - [Python API Usage](#python-api-usage-1)\r\n - [Understanding Pitch and Resolution](#understanding-pitch-and-resolution)\r\n - [Exporting Results](#exporting-results)\r\n - [Command Line Usage](#command-line-usage-2)\r\n - [Animation Generation](#animation-generation)\r\n - [Experiment Management](#experiment-management)\r\n - [Command Line Options](#command-line-options)\r\n - [Acknowledgements](#acknowledgements)\r\n - [Citation](#citation)\r\n\r\n## Overview\r\n\r\nThis code performs 3D structural topology optimization using the SIMP (Solid Isotropic Material with Penalization) method. It is designed to be efficient by utilizing:\r\n\r\n- Parallel solver (PyPardiso if available, otherwise SciPy's spsolve)\r\n- Precomputed assembly mapping for fast matrix assembly\r\n- Support for obstacle regions where no material can be placed\r\n- Flexible obstacle configuration via JSON files\r\n- Advanced visualization capabilities including animation generation\r\n\r\n## Installation\r\n\r\n1. Clone this repository:\r\n```bash\r\ngit clone https://github.com/jihoonkim888/PyTopo3D.git\r\ncd PyTopo3D\r\n```\r\n\r\n2. Create and activate the conda environment:\r\n```bash\r\n# Create the environment from the environment.yml file\r\nconda env create -f environment.yml\r\n\r\n# Activate the environment\r\nconda activate pytopo3d\r\n```\r\n\r\n## Basic Usage\r\n\r\n### Configuration Parameters\r\n\r\nThe main optimization parameters are:\r\n\r\n- `nelx`, `nely`, `nelz`: Number of elements in x, y, z directions (default: 60, 30, 20)\r\n- `volfrac`: Volume fraction constraint (0.0-1.0) (default: 0.3)\r\n- `penal`: Penalization power for SIMP method (default: 3.0)\r\n- `rmin`: Filter radius for sensitivity filtering (default: 3.0)\r\n- `disp_thres`: Display threshold for 3D visualization (elements with density > disp_thres are shown) (default: 0.5)\r\n- `tolx`: Convergence tolerance on design change (default: 0.01)\r\n- `maxloop`: Maximum number of iterations (default: 2000)\r\n\r\n### Command-line Interface\r\n\r\nTo run a basic optimization:\r\n\r\n```bash\r\npython main.py --nelx 32 --nely 16 --nelz 16 --volfrac 0.3 --penal 3.0 --rmin 3.0\r\n```\r\n\r\nFor full options:\r\n\r\n```bash\r\npython main.py --help\r\n```\r\n\r\n### Python Package API\r\n\r\n```python\r\nimport numpy as np\r\nfrom pytopo3d.core.optimizer import top3d\r\n\r\n# Define parameters\r\nnelx, nely, nelz = 32, 16, 16\r\nvolfrac = 0.3\r\npenal = 3.0\r\nrmin = 3.0\r\ndisp_thres = 0.5\r\n\r\n# Run optimization\r\nresult = top3d(nelx, nely, nelz, volfrac, penal, rmin, disp_thres)\r\n\r\n# Save result\r\nnp.save(\"optimized_design.npy\", result)\r\n```\r\n\r\n## Advanced Features\r\n\r\n### Obstacle Configuration\r\n\r\nPyTopo3D supports defining regions where material should not be placed during optimization.\r\n\r\n#### Command Line Usage\r\n\r\n```bash\r\npython main.py --obstacle-config examples/obstacles_config_cylinder.json\r\n```\r\n\r\n#### Python API Usage\r\n\r\n```python\r\n# Create a custom obstacle mask\r\nobstacle_mask = np.zeros((nely, nelx, nelz), dtype=bool)\r\nobstacle_mask[5:15, 3:7, 3:7] = True # Example obstacle\r\n\r\n# Or load obstacles from config file\r\nfrom pytopo3d.preprocessing.geometry import load_geometry_data\r\n\r\ndesign_space_mask, obstacle_mask, combined_obstacle_mask = load_geometry_data(\r\n nelx=nelx, \r\n nely=nely, \r\n nelz=nelz, \r\n obstacle_config=\"path/to/config.json\"\r\n)\r\n\r\n# Use the mask in optimization\r\nresult = top3d(nelx, nely, nelz, volfrac, penal, rmin, disp_thres, \r\n obstacle_mask=combined_obstacle_mask)\r\n```\r\n\r\n#### Obstacle Configuration Format\r\n\r\nThe obstacle configuration file is a JSON file with the following structure:\r\n\r\n```json\r\n{\r\n \"obstacles\": [\r\n {\r\n \"type\": \"cube\",\r\n \"center\": [0.5, 0.5, 0.2], // x, y, z as fractions [0-1]\r\n \"size\": 0.15 // single value for a cube\r\n },\r\n {\r\n \"type\": \"sphere\",\r\n \"center\": [0.25, 0.25, 0.6],\r\n \"radius\": 0.1\r\n },\r\n {\r\n \"type\": \"cylinder\",\r\n \"center\": [0.75, 0.5, 0.5],\r\n \"radius\": 0.08,\r\n \"height\": 0.7,\r\n \"axis\": 2 // 0=x, 1=y, 2=z\r\n },\r\n {\r\n \"type\": \"cube\",\r\n \"center\": [0.25, 0.75, 0.5],\r\n \"size\": [0.15, 0.05, 0.3] // [x, y, z] for a cuboid\r\n }\r\n ]\r\n}\r\n```\r\n\r\nSupported obstacle types:\r\n- `cube`: A cube or cuboid. Use `size` as a single value for a cube, or as `[x, y, z]` for a cuboid.\r\n- `sphere`: A sphere. Use `radius` to set the size.\r\n- `cylinder`: A cylinder. Use `radius`, `height`, and `axis` (0=x, 1=y, 2=z) to configure.\r\n\r\nAll positions are specified as fractions [0-1] of the domain size, making it easy to reuse configurations across different mesh resolutions.\r\n\r\n### Design Space Customization\r\n\r\nPyTopo3D allows using STL files to define the design space geometry, enabling complex shapes beyond the standard rectangular domain.\r\n\r\n#### Command Line Usage\r\n\r\n```bash\r\npython main.py --design-space-stl path/to/design_space.stl --pitch 0.5\r\n```\r\n\r\nCommand line options:\r\n- `--design-space-stl`: Path to an STL file defining the design space geometry\r\n- `--pitch`: Distance between voxel centers when voxelizing STL (default: 1.0, smaller values create finer detail)\r\n- `--invert-design-space`: Flag to invert the design space (treat STL as void space rather than design space)\r\n\r\n#### Python API Usage\r\n\r\n```python\r\nfrom pytopo3d.preprocessing.geometry import load_geometry_data\r\nimport numpy as np\r\n\r\n# Load design space from STL\r\ndesign_space_mask, obstacle_mask, combined_obstacle_mask = load_geometry_data(\r\n nelx=60, \r\n nely=30, \r\n nelz=20,\r\n design_space_stl=\"path/to/design_space.stl\",\r\n pitch=0.5,\r\n invert_design_space=False\r\n)\r\n\r\n# The shape of the mask is determined by the STL geometry and pitch\r\nnely, nelx, nelz = design_space_mask.shape\r\nprint(f\"Resolution from voxelization: {nely}x{nelx}x{nelz}\")\r\n\r\n# Use the mask in optimization\r\nfrom pytopo3d.core.optimizer import top3d\r\n\r\nresult = top3d(\r\n nelx=nelx, \r\n nely=nely, \r\n nelz=nelz, \r\n volfrac=0.3, \r\n penal=3.0, \r\n rmin=3.0,\r\n disp_thres=0.5,\r\n obstacle_mask=combined_obstacle_mask\r\n)\r\n```\r\n\r\n#### Understanding Pitch and Resolution\r\n\r\nThe `pitch` parameter directly controls the resolution of the voxelized model:\r\n\r\n- Smaller pitch values create higher resolution voxelizations\r\n- The number of voxels along any dimension = physical length \u00f7 pitch\r\n- Choose pitch value based on the level of detail needed and computational resources available\r\n\r\n### Exporting Results\r\n\r\nYou can export the final optimization result as an STL file for 3D printing or further analysis in CAD software.\r\n\r\n#### Command Line Usage\r\n\r\n```bash\r\npython main.py --nelx 32 --nely 16 --nelz 16 \\\r\n --volfrac 0.3 --penal 3.0 --rmin 3.0 \\\r\n --export-stl \\\r\n [--stl-level 0.5] \\\r\n [--smooth-stl] \\\r\n [--smooth-iterations 5]\r\n```\r\n\r\nOptions:\r\n- `--export-stl`: Flag to enable STL export of the final optimization result\r\n- `--stl-level`: Contour level for the marching cubes algorithm (default: 0.5)\r\n- `--smooth-stl`: Flag to apply Laplacian smoothing to the mesh (default: True)\r\n- `--smooth-iterations`: Number of iterations for mesh smoothing (default: 5)\r\n\r\n### Animation Generation\r\n\r\nPyTopo3D can generate animations of the optimization process.\r\n\r\n```bash\r\npython main.py --nelx 32 --nely 16 --nelz 16 \\\r\n --create-animation \\\r\n --animation-frequency 10 \\\r\n --animation-frames 50 \\\r\n --animation-fps 5\r\n```\r\n\r\nOptions:\r\n- `--create-animation`: Flag to enable animation generation\r\n- `--animation-frequency`: Store every N iterations for the animation (default: 10)\r\n- `--animation-frames`: Target number of frames in the final animation (default: 50)\r\n- `--animation-fps`: Frames per second in the generated animation (default: 5)\r\n\r\n### Experiment Management\r\n\r\nPyTopo3D includes a robust experiment management system that automatically:\r\n\r\n- Creates a uniquely named directory for each optimization run\r\n- Saves all relevant parameters, inputs, and outputs\r\n- Generates detailed logs of the optimization process\r\n- Records performance metrics and convergence data\r\n\r\n#### Command Line Options\r\n\r\n```bash\r\npython main.py --experiment-name custom_name \\\r\n --description \"Detailed description of this experiment\" \\\r\n --log-level DEBUG \\\r\n --log-file custom_log.log \\\r\n --verbose\r\n```\r\n\r\nOptions:\r\n- `--experiment-name`: Custom name for the experiment (optional, auto-generated if not provided)\r\n- `--description`: Description of the experiment stored in the results metadata\r\n- `--log-level`: Set logging detail level (DEBUG, INFO, WARNING, ERROR, CRITICAL)\r\n- `--log-file`: Path to a custom log file\r\n- `--verbose`: Enable more detailed output (sets log level to DEBUG)\r\n- `--quiet`: Reduce output verbosity (sets log level to WARNING)\r\n\r\n## Acknowledgements\r\n\r\nThis code is adapted from [Liu & Tovar's MATLAB code](https://www.top3d.app/) for 3D topology optimization.\r\n\r\n> K. Liu and A. Tovar, \"An efficient 3D topology optimization code written in Matlab\", Struct Multidisc Optim, 50(6): 1175-1196, 2014, doi:10.1007/s00158-014-1107-x\r\n\r\n## Citation\r\n\r\nIf you use PyTopo3D in your research or work, please cite our paper on ArXiv: [PyTopo3D: A Python Framework for 3D SIMP-based Topology Optimization](https://arxiv.org/abs/2504.05604)\r\n\r\n> Kim, J. & Kang, N. (2024). PyTopo3D: A Python Framework for 3D SIMP-based Topology Optimization. arXiv preprint arXiv:2504.05604.\r\n\r\n```bibtex\r\n@article{kim2025pytopo3d\r\n title={PyTopo3D: A Python Framework for 3D SIMP-based Topology Optimization}, \r\n author={Jihoon Kim and Namwoo Kang},\r\n journal={arXiv preprint arXiv:2504.05604},\r\n year={2025}\r\n}\r\n```\r\n\r\nThis paper provides a detailed explanation of the implementation, theoretical foundations, and optimizations used in PyTopo3D. Proper citation helps support the continued development of open-source scientific software.\r\n",
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