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This paper provides a simple, compact and efficient 90-line pedagogical MATLAB code for topology optimization using hexagonal elements (honeycomb tessellation). Hexagonal elements provide nonsingular connectivity between two juxtaposed…

Computational Engineering, Finance, and Science · Computer Science 2022-05-03 Prabhat Kumar

Python is a low-cost and open-source substitute for the MATLAB programming language. This paper presents ``\texttt{PyTOPress}", a compact Python code meant for pedagogical purposes for topology optimization for structures subjected to…

Computational Engineering, Finance, and Science · Computer Science 2025-02-04 Shivajay Saxena , Swagatam Islam Sarkar , Prabhat Kumar

This paper presents an efficient 51 lines Matlab code to solve topology optimization problems. By the fact that the presented code is based on an hard 0-1 optimization method that handles the integer part of the optimization in a simple…

Optimization and Control · Mathematics 2019-02-05 Vittorio Latorre

This work presents an 808-line Matlab educational code for combined multi-scale topology optimisation and phasor-based dehomogenisation titled deHomTop808. The multi-scale formulation utilises homogenisation of optimal microstructures to…

Mathematical Software · Computer Science 2024-05-27 Rebekka Varum Woldseth , Ole Sigmund , Peter Dørffler Ladegaard Jensen

Three-dimensional topology optimization (TO) is a powerful technique in engineering design, but readily usable, open-source implementations remain limited within the popular Python scientific environment. This paper introduces PyTopo3D, a…

Graphics · Computer Science 2025-04-09 Jihoon Kim , Namwoo Kang

This paper presents an efficient and comprehensive MATLAB code to solve two-dimensional structural topology optimization problems, including minimum mean compliance, compliant mechanism synthesis and multi-load compliance problems. The…

Computational Engineering, Finance, and Science · Computer Science 2021-07-19 Daniel Yago , Juan Cante , Oriol Lloberas-Valls , Javier Oliver

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…

Mathematical Software · Computer Science 2020-12-16 Abhinav Gupta , Rajib Chowdhury , Anupam Chakrabarti , Timon Rabczuk

Convex optimization encompasses a wide range of optimization problems that contain many efficiently solvable subclasses. Interior point methods are currently the state-of-the-art approach for solving such problems, particularly effective…

Optimization and Control · Mathematics 2025-03-28 Andreas Klingler , Tim Netzer

In this study, we describe a procedure of topology optimization in the framework of the linear Boltzmann equation, implemented using a reference Monte-Carlo particle transport code. This procedure can design complex structures that optimize…

Instrumentation and Detectors · Physics 2019-08-20 Sébastien Chabod

In recent years, topology optimization (TO) has gained widespread attention as a powerful structural design method. However, its application remains challenging due to the deep expertise and extensive development effort required.…

Analysis of PDEs · Mathematics 2025-05-06 Liang He , Huayi Wei , Tian Tian

We provide a compact 200 line MATLAB code demonstrating how topology optimization (TopOpt) as an inverse design tool may be used in photonics, targeting the design of two-dimensional dielectric metalenses and a metallic reflector as…

Mathematical Software · Computer Science 2021-02-24 Rasmus E. Christiansen , Ole Sigmund

Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches…

Optimization and Control · Mathematics 2015-03-10 Igor Ostanin , Denis Zorin , Ivan Oseledets

A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-gradient method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is…

Computational Engineering, Finance, and Science · Computer Science 2016-05-30 Emre Biyikli , Albert C. To

Topology optimization using gradient search with negative and positive elliptical masks and honeycomb tessellation is presented. Through a novel skeletonization algorithm for topologies defined using filled and void hexagonal…

Computational Engineering, Finance, and Science · Computer Science 2020-10-13 Nikhil Singh , Prabhat Kumar , Anupam Saxena

This paper presents a Material Mask Overlay topology optimization approach with the improved material assignment at the element level for achieving the desired discreteness of the optimized designs for pressure-loaded problems. Hexagonal…

Computational Engineering, Finance, and Science · Computer Science 2022-10-17 Prabhat Kumar , Anupam Saxena

We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to…

Computational Engineering, Finance, and Science · Computer Science 2022-08-24 Davide Cortellessa , Nicola Ferro , Simona Perotto , Stefano Micheletti

We design and implement a Python library to help the non-expert using all these powerful tools in a way that is efficient, extensible, and simple to incorporate into the workflow of the data scientist, practitioner, and applied researcher.…

Optimization and Control · Mathematics 2022-04-13 Mario Lezcano-Casado

In this paper, we propose a topology optimization (TO) framework where the design is parameterized by a set of convex polygons. Extending feature mapping methods in TO, the representation allows for direct extraction of the geometry. In…

Optimization and Control · Mathematics 2023-05-09 Aaditya Chandrasekhar

Presently, topology optimization requires multiple iterations to create an optimized structure for given conditions. Among the conditions for topology optimization,the design area is one of the most important for structural design. In this…

Computational Engineering, Finance, and Science · Computer Science 2020-04-21 Keigo Nakamura , Yoshiro Suzuki

Hyperparameter tuning is a fundamental aspect of machine learning research. Setting up the infrastructure for systematic optimization of hyperparameters can take a significant amount of time. Here, we present PyHopper, a black-box…

Machine Learning · Computer Science 2022-10-11 Mathias Lechner , Ramin Hasani , Philipp Neubauer , Sophie Neubauer , Daniela Rus
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