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Concepts from quantum topological states of matter have been extensively utilized in the past decade in creating mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized…

Applied Physics · Physics 2022-07-14 Haning Xiu , Harry Liu , Andrea Poli , Guangchao Wan , Ellen M. Arruda , Xiaoming Mao , Zi Chen

In this study, we investigate and compare formulations for computing shape derivatives in bi-material level-set optimization with precise modeling of the interface. The level-set function is parameterized using B-splines, whose coordinates…

Classical Physics · Physics 2024-10-30 Majd Kosta , Oded Amir

In this paper, we propose a level set-based topology optimization method for the unit-cell design of acoustic metasurfaces by using a two-scale homogenization method. Based on previous works, we first propose a homogenization method for…

Computational Engineering, Finance, and Science · Computer Science 2021-06-23 Yuki Noguchi , Takayuki Yamada

A topology optimization problem in a phase field setting is considered to obtain rigid structures, which are resilient to external forces and constructable with additive manufacturing. Hence, large deformations of overhangs due to gravity…

Optimization and Control · Mathematics 2026-02-24 Luise Blank , Maximilian Urmann

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

We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…

Optimization and Control · Mathematics 2025-12-17 Yixin Tan , Fang Feng , Shengfeng Zhu

Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…

Optimization and Control · Mathematics 2015-07-22 Arun L. Gain , Glaucio H. Paulino , Leonardo Duarte , Ivan F. M. Menezes

This work presents a scalable computational framework for optimal design under uncertainty with application to multi-material insulation components of building envelopes. The forward model consists of a multi-phase thermo-mechanical model…

Optimization and Control · Mathematics 2023-04-20 Jingye Tan , Danial Faghihi

It is important to accurately model materials' properties at lower length scales (micro-level) while translating the effects to the components and/or system level (macro-level) can significantly reduce the amount of experimentation required…

Computers and Society · Computer Science 2022-11-08 Kazuma Kobayashi , Shoaib Usman , Carlos Castano , Dinesh Kumar , Syed Alam

We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…

Numerical Analysis · Mathematics 2026-05-15 Peter Gangl , Brendan Keith , Dohyun Kim , Boyan S. Lazarov , Thomas M. Surowiec

Topology optimization of modular structures and mechanisms enables balancing the performance of automatically-generated individualized designs, as required by Industry 4.0, with enhanced sustainability by means of component reuse. For…

Materials Science · Physics 2022-05-25 Marek Tyburec , Martin Doškář , Jan Zeman , Martin Kružík

In this paper, a hybrid Lagrangian-Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian…

Computational Physics · Physics 2021-04-14 Yue Li , Xuan Li , Minchen Li , Yixin Zhu , Bo Zhu , Chenfanfu Jiang

This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the…

Optimization and Control · Mathematics 2019-01-30 Grigor Nika , Andrei Constantinescu

A new approach for generating stress-constrained topological designs in continua is presented. The main novelty is in the use of elasto-plastic modeling and in optimizing the design such that it will exhibit a linear-elastic response. This…

Computational Engineering, Finance, and Science · Computer Science 2016-08-25 Oded Amir

A novel computational framework for designing metamaterials with negative Poisson's ratio over a large strain range is presented in this work by combining the density-based topology optimization together with a mixed stress/deformation…

Computational Engineering, Finance, and Science · Computer Science 2019-07-31 Guodong Zhang , Kapil Khandelwal

Multiscale topology optimization is crucial for designing porous infill structures with high stiffness-to-weight ratios and excellent energy absorption. Although gradient-based methods provide a rigorous framework, they are computationally…

Optimization and Control · Mathematics 2025-10-13 Shuzhi Xu , Yifan Guo , Hiroki Kawabe , Kentaro Yaji

In the present work, a highly efficient Moving Morphable Component (MMC) based approach for multi-resolution topology optimization is proposed. In this approach, high-resolution optimization results can be obtained with much less number of…

Computational Engineering, Finance, and Science · Computer Science 2018-12-10 Chang Liu , Yichao Zhu , Zhi Sun , Dingding Li , Zongliang Du , Weisheng Zhang , Xu Guo

The increasing availability of full-field displacement data from imaging techniques in experimental mechanics is determining a gradual shift in the paradigm of material model calibration and discovery, from using several simple-geometry…

Computational Engineering, Finance, and Science · Computer Science 2025-07-01 Saeid Ghouli , Moritz Flaschel , Siddhant Kumar , Laura De Lorenzis

Topology optimization (TO) in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized (SIMP) methods…

Computational Engineering, Finance, and Science · Computer Science 2025-07-28 Gabriel Stankiewicz , Chaitanya Dev , Paul Steinmann

When electrically stimulated, electroactive polymers (EAPs) respond with mechanical deformation. The goal of this work is to design electrode and EAP layouts simultaneously in structures by using density-based, multi-material topology…

Computational Engineering, Finance, and Science · Computer Science 2024-12-05 Daniel Hård , Mathias Wallin , Matti Ristinmaa