This paper presents a 55-line code written in python for 2D and 3D topology optimization (TO) based on the open-source finite element computing software (FEniCS), equipped with various finite element tools and solvers. PETSc is used as the linear algebra back-end, which results in significantly less computational time than standard python libraries. The code is designed based on the popular solid isotropic material with penalization (SIMP) methodology. Extensions to multiple load cases, different boundary conditions, and incorporation of passive elements are also presented. Thus, this implementation is the most compact implementation of SIMP based topology optimization for 3D as well as 2D problems. Utilizing the concept of Euclidean distance matrix to vectorize the computation of the weight matrix for the filter, we have achieved a substantial reduction in the computational time and have also made it possible for the code to work with complex ground structure configurations. We have also presented the code's extension to large-scale topology optimization problems with support for parallel computations on complex structural configuration, which could help students and researchers explore novel insights into the TO problem with dense meshes. Appendix-A contains the complete code, and the website: \url{https://github.com/iitrabhi/topo-fenics} also contains the complete code.

中文翻译：

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用于2D和3D大规模并行拓扑优化的55行代码

本文基于开放源代码有限元计算软件（FEniCS），提供了用python编写的用于2D和3D拓扑优化（TO）的55行代码，并配备了各种有限元工具和求解器。PETSc用作线性代数后端，与标准python库相比，其计算时间显着减少。该代码是根据流行的固态各向同性材料采用惩罚（SIMP）方法设计的。还介绍了对多种载荷工况，不同边界条件以及无源元件的结合的扩展。因此，此实现是针对3D和2D问题的基于SIMP拓扑优化的最紧凑的实现。利用欧几里得距离矩阵的概念对滤波器权重矩阵的计算进行矢量化处理，我们大大减少了计算时间，并使代码可以用于复杂的地面结构配置。我们还介绍了代码对大规模拓扑优化问题的扩展，并支持对复杂结构配置的并行计算，这可以帮助学生和研究人员探索有关密集网格TO问题的新颖见解。附录A包含完整的代码，网站：\ url {https://github.com/iitrabhi/topo-fenics}也包含完整的代码。支持复杂结构配置的并行计算，从而扩展了大规模拓扑优化问题，可以帮助学生和研究人员探索有关密集网格TO问题的新颖见解。附录A包含完整的代码，网站：\ url {https://github.com/iitrabhi/topo-fenics}也包含完整的代码。支持复杂结构配置的并行计算，从而扩展了大规模拓扑优化问题，可以帮助学生和研究人员探索有关密集网格TO问题的新颖见解。附录A包含完整的代码，网站：\ url {https://github.com/iitrabhi/topo-fenics}也包含完整的代码。