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The paper presents a novel, parameter free, density evaluation method for topology optimization based on normalized product of a scalar field. The approach imposes length scale on solid phase implicitly and allows for pure 0-1 singularity…

Mathematical Physics · Physics 2022-08-25 Nikhil Singh , Anupam Saxena

This paper presents a density-based topology optimization approach to design structures under self-weight load. Such loads change their magnitude and/or location as the topology optimization advances and pose several unique challenges,…

Computational Engineering, Finance, and Science · Computer Science 2022-04-26 Prabhat Kumar

The robust topology optimization formulation that introduces the eroded and dilated versions of the design has gained increasing popularity in recent years, mainly because of its ability to produce designs satisfying a minimum length scale.…

Optimization and Control · Mathematics 2021-04-16 Denis Trillet , Pierre Duysinx , Eduardo Fernández

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

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the…

Optimization and Control · Mathematics 2021-03-30 Jorge L. Barrera , Markus J. Geiss , Kurt Maute

The need for optimized structures with good mechanical performance for the minimum weight is common in industry. Solid Isotropic Material with Penalization (SIMP) is a Topology Optimization (TO) method offering a trade-off between minimum…

Optimization and Control · Mathematics 2025-03-28 Luis Irastorza-Valera , Ricardo Larraínzar-Garijo , Javier Montoya-Adárraga , Luis Saucedo-Mora

A method is created to automatically increase the threshold projection parameter in three-field density-based topology optimization to achieve a near binary design. The parameter increase each iteration is based on an exponential growth…

Optimization and Control · Mathematics 2024-04-23 Peter Donald Dunning

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

In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…

Computational Engineering, Finance, and Science · Computer Science 2019-10-09 Nicolò Pollini , Oded Amir

In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness…

Computational Engineering, Finance, and Science · Computer Science 2023-07-31 Rafael Merli , Antolín Martínez-Martínez , Juan José Ródenas , Marc Bosch-Galera , Enrique Nadal

Two approaches that use a density field for seeding holes in level set topology optimization are proposed. In these approaches, the level set field describes the material-void interface while the density field describes the material…

Optimization and Control · Mathematics 2019-09-25 Jorge L. Barrera , Markus J. Geiss , Kurt Maute

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

We propose a direct mesh-free method for performing topology optimization by integrating a density field approximation neural network with a displacement field approximation neural network. We show that this direct integration approach can…

Computational Engineering, Finance, and Science · Computer Science 2023-09-26 Aditya Joglekar , Hongrui Chen , Levent Burak Kara

Density-based topology optimization methods such as SIMP enable efficient topological exploration but produce diffuse material boundaries that require interpretation before manufacturing. Level-set methods maintain sharp interfaces but are…

Computational Engineering, Finance, and Science · Computer Science 2026-05-07 Ondřej Ježek , Ján Kopačka , Martin Isoz , Dušan Gabriel

This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…

Optimization and Control · Mathematics 2025-07-23 Huangxin Chen , Piaopiao Dong , Dong Wang , Xiao-Ping Wang

Topology optimization (TO) can be viewed as seeking an optimal solution in the design space of a given TO problem. For weakly non-linear TO problems, e.g., compliance minimization, sensitivity-based methods typically converge well, whereas…

Optimization and Control · Mathematics 2026-03-25 Ziliang Wang , Jiahua Wu , Jun Yang , Shintaro Yamasaki

A feature-mapping framework for inverse reconstruction of density-based topology optimization results is proposed. Unlike SIMP, whose voxelized outputs are hard to interpret or reuse, the method represents designs with high-level geometric…

Optimization and Control · Mathematics 2026-02-16 Patrick Jung

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 density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…

Computational Engineering, Finance, and Science · Computer Science 2019-08-29 Yuqing Zhou , Tsuyoshi Nomura , Ercan M. Dede , Kazuhiro Saitou

In the present work we introduce a novel graded-material design based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material…

Optimization and Control · Mathematics 2019-06-03 Massimo Carraturo , Elisabetta Rocca , Elena Bonetti , Dietmar Hömberg , Alessandro Reali , Ferdinando Auricchio
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