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Although design optimization has shown its great power of automatizing the whole design process and providing an optimal design, using sophisticated computational models, its process can be formidable due to a computationally expensive…

Numerical Analysis · Mathematics 2019-09-26 Youngsoo Choi , Geoffrey Oxberry , Daniel White , Trenton Kirchdoerfer

The work provides an exhaustive comparison of some representative families of topology optimization methods for 3D structural optimization, such as the Solid Isotropic Material with Penalization (SIMP), the Level-set, the Bidirectional…

Computational Engineering, Finance, and Science · Computer Science 2021-08-09 Daniel Yago , Juan Cante , Oriol Lloberas-Valls , Javier Oliver

We present a new method that efficiently solves TO problems and provides a practical pathway to leverage quantum computing to exploit potential quantum advantages. This work targets on large-scale, multi-material TO challenges for…

Computational Physics · Physics 2026-01-16 Zisheng Ye , Wenxiao Pan

Projected Gradient Descent (PGD) methods offer a simple and scalable approach to topology optimization (TO), yet they often struggle with nonlinear and multi-constraint problems due to the complexity of active-set detection. This paper…

Computational Engineering, Finance, and Science · Computer Science 2025-11-19 Amin Heyrani Nobari , Faez Ahmed

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

Topology optimization(TO) is widely used in engineering because of its ability to save material and optimize structural performance. Although prior work has explored 2D human-centered design tool for TO, the results are often limited in…

Human-Computer Interaction · Computer Science 2026-04-24 Shuyue Feng , Cedric Caremel , Yoshihiro Kawahara

Topology optimization (TO) is employed in engineering to optimize structural performance while maximizing material efficiency. However, traditional TO methods incur significant computational and time costs. Although research has leveraged…

Human-Computer Interaction · Computer Science 2026-03-20 Shuyue Feng , Cedric Caremel , Yoshihiro Kawahara

Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…

Computational Engineering, Finance, and Science · Computer Science 2020-04-14 Marco K. Swierstra , Deepak K. Gupta , Matthijs Langelaar

This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…

Optimization and Control · Mathematics 2020-04-22 Shanglong Zhang , Arun L. Gain , Julian A. Norato

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Numerical Analysis · Mathematics 2024-05-15 Nicola Rares Franco , Andrea Manzoni , Paolo Zunino , Jan S. Hesthaven

This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with imprecise probability is integrated into the…

Computational Engineering, Finance, and Science · Computer Science 2020-03-10 Y. Wu , Eric Li , Z. C. He , X. Y. Lin , H. X. Jiang

Topology optimization (TO) has experienced a dramatic development over the last decades aided by the arising of metamaterials and additive manufacturing (AM) techniques, and it is intended to achieve the current and future challenges. In…

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

Engineers learn from every design they create, building intuition that helps them quickly identify promising solutions for new problems. Topology optimization (TO) - a well-established computational method for designing structures with…

Computational Engineering, Finance, and Science · Computer Science 2025-02-05 Igor Kuszczak , Gawel Kus , Federico Bosi , Miguel A. Bessa

In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…

Optimization and Control · Mathematics 2022-02-03 Wendong Huo , Chang Liu , Zongliang Du , Xudong Jiang , Zhengyu Liu , Xu Guo

Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the…

Machine Learning · Computer Science 2025-06-18 Andreas Radler , Eric Volkmann , Johannes Brandstetter , Arturs Berzins

Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited…

Computational Engineering, Finance, and Science · Computer Science 2023-06-30 Changyoung Yuhn , Yuki Sato , Hiroki Kobayashi , Atsushi Kawamoto , Tsuyoshi Nomura

Explicit topology optimization methods have received ever-increasing interest in recent years. In particular, a 188-line Matlab code of the two-dimensional (2D) Moving Morphable Component (MMC)-based topology optimization method was…

Optimization and Control · Mathematics 2022-05-31 Zongliang Du , Tianchen Cui , Chang Liu , Weisheng Zhang , Yilin Guo , Xu Guo

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

The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…

Computational Engineering, Finance, and Science · Computer Science 2017-08-25 Dengyang Zhao , Ming Li , Yusheng Liu