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This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…

Numerical Analysis · Mathematics 2019-09-25 L. Noel , M. Schmidt , C. Messe , J. A. Evans , K. Maute

This work presents a multilevel approach to large--scale topology optimization accounting for linearized buckling criteria. The method relies on the use of preconditioned iterative solvers for all the systems involved in the linear buckling…

Numerical Analysis · Mathematics 2020-03-03 Federico Ferrari , Ole Sigmund

A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…

Optimization and Control · Mathematics 2015-05-13 Andreas Adelmann , Peter Arbenz , Andrew Foster , Yves Ineichen

Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. The majority of…

Machine Learning · Computer Science 2024-08-08 Amin Yousefpour , Shirin Hosseinmardi , Carlos Mora , Ramin Bostanabad

This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…

Computational Engineering, Finance, and Science · Computer Science 2020-06-16 Zhi Zeng , Fulei Ma

Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for…

This paper presents a highly efficient method to obtain high-resolution, near-optimal 3D topologies optimized for minimum compliance on a standard PC. Using an implicit geometry description we derive a single-scale interpretation of optimal…

Computational Engineering, Finance, and Science · Computer Science 2020-04-22 Jeroen Groen , Florian Stutz , Niels Aage , J. Andreas Bærentzen , Ole Sigmund

Designing metamaterials for extreme mechanical behavior involves the optimal selection of design parameters. However, identifying these optimal parameters through topology optimization (TO) across a large parametric space requires extensive…

Computational Physics · Physics 2025-11-10 Ajendra Singh , Shubham Saurabh , Abhinav Gupta , Rajib Chowdhury

This paper presents a multicomponent topology optimization method for designing structures assembled from additively-manufactured components, considering anisotropic material behavior for each component due to its build orientation,…

Computational Engineering, Finance, and Science · Computer Science 2019-11-26 Yuqing Zhou , Tsuyoshi Nomura , Kazuhiro Saitou

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

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

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

Computational Engineering, Finance, and Science · Computer Science 2024-02-23 Connor N. Mallon , Aaron W. Thornton , Matthew R. Hill , Santiago Badia

This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design…

Computational Engineering, Finance, and Science · Computer Science 2024-08-29 Hiroki Kobayashi , Katsuya Nomura , Yuqing Zhou , Masato Tanaka , Atsushi Kawamoto , Tsuyoshi Nomura

Structural optimization (topology, shapes, sizing) is an important tool for facilitating the emergence of new concepts in structural design. Normally, topology optimization is carried out at the early stage of design and then shape and…

Optimization and Control · Mathematics 2021-03-16 Ghislain Raze , Joseph Morlier

Element-based topology optimization algorithms capable of generating smooth boundaries have drawn serious attention given the significance of accurate boundary information in engineering applications. The basic framework of a new…

Computational Engineering, Finance, and Science · Computer Science 2021-01-11 Yun-Fei Fu , Bernard Rolfe , Ngai Sum Louis Chiu , Yanan Wang , Xiaodong Huang , Kazem Ghabraie

Developing appropriate analytic-function-based constitutive models for new materials with nonlinear mechanical behavior is demanding. For such kinds of materials, it is more challenging to realize the integrated design from the collection…

Optimization and Control · Mathematics 2022-11-11 Yunhang Guo , Zongliang Du , Lubin Wang , Wen Meng , Tien Zhang , Ruiyi Su , Dongsheng Yang , Shan Tang , Xu Guo

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded…

Machine Learning · Computer Science 2025-10-29 Amin Heyrani Nobari , Lyle Regenwetter , Cyril Picard , Ligong Han , Faez Ahmed

This paper presents a comparative analysis of algorithmic strategies for fitting tessellation models to 3D image data of materials such as polycrystals and foams. In this steadily advancing field, we review and assess optimization-based…

Computer Vision and Pattern Recognition · Computer Science 2025-07-22 Andreas Alpers , Orkun Furat , Christian Jung , Matthias Neumann , Claudia Redenbach , Aigerim Saken , Volker Schmidt

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

We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order…

Other Condensed Matter · Physics 2022-05-31 Bastian Telgen , Ole Sigmund , Dennis M. Kochmann