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Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bends{\o}e and Kikuchi from 1988, which…

Computational Engineering, Finance, and Science · Computer Science 2023-05-01 Christoffer Fyllgraf Christensen , Fengwen Wang , Ole Sigmund

Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the…

Computational Engineering, Finance, and Science · Computer Science 2019-09-06 Jun Wu , Weiming Wang , Xifeng Gao

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

This paper considers the design of structures made of engineered materials, accounting for uncertainty in material properties. We present a topology optimization approach that optimizes the structural shape and topology at the macroscale…

Optimization and Control · Mathematics 2021-10-27 Subhayan De , Kurt Maute , Alireza Doostan

Functionally Graded Materials (FGMs) made of soft constituents have emerged as promising material-structure systems in potential applications across many engineering disciplines, such as soft robots, actuators, energy harvesting, and tissue…

Computational Engineering, Finance, and Science · Computer Science 2025-07-01 Shiguang Deng , Horacio D. Espinosa , Wei Chen

A multiobjective optimization method is proposed for obtaining the optimal plane trusses simultaneously for various aspect ratios of the initial ground structure as a set of Pareto optimal solutions generated through a single optimization…

Optimization and Control · Mathematics 2023-08-01 Makoto Ohsaki , Saku Aoyagi , Kazuki Hayashi

Self-assembly is one of the prevalent strategies used by living systems to fabricate ensembles of precision nanometer-scale structures and devices. The push for analogous approaches to create synthetic nanomaterials has led to the…

Material microstructures are traditionally compared using sets of statistical measures that are incomplete, e.g., two visually distinct microstructures can have identical grain size distributions and phase fractions. While this is not a…

Computational Physics · Physics 2025-10-14 Dylan Miley , Ethan Suwandi , Benjamin Schweinhart , Jeremy K Mason

In this review we identify a new category of structural optimization methods that has emerged over the last 20 years, which we propose to call feature-mapping methods. The two defining aspects of these methods are that the design is…

Optimization and Control · Mathematics 2019-10-25 Fabian Wein , Peter Dunning , Julián A. Norato

In this paper, we develop a rigorous mathematical framework for the optimization of hip roof house geometry, with the primary goal of minimizing the external surface of the building envelope for a given set of design constraints. Five…

Optimization and Control · Mathematics 2026-01-21 Ewa Rokita-Magdziarz , Barbara Gronostajska , Marcin Magdziarz

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

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…

Trusses are load-carrying light-weight structures consisting of bars connected at joints ubiquitously applied in a variety of engineering scenarios. Designing optimal trusses that satisfy functional specifications with a minimal amount of…

Graphics · Computer Science 2019-01-18 Caigui Jiang , Chengcheng Tang , Hans-Peter Seidel , Renjie Chen , Peter Wonka

In this paper we apply topology optimization to micro-structured superhydrophobic surfaces for the first time. It has been experimentally observed that a droplet suspended on a brush of micrometric posts shows a high static contact angle…

Soft Condensed Matter · Physics 2013-02-28 A. Cavalli , P. Bøggild , F. Okkels

The paper presents a concept/technique to compress and synthesize complex material morphologies that is based on Wang tilings. Specifically, a microstructure is stored in a set of Wang tiles and its reconstruction is performed by means of a…

Materials Science · Physics 2014-12-18 Martin Doškář , Jan Novák , Jan Zeman

The paper is devoted to the shape optimization of microstructures generating porous locally periodic materials saturated by viscous fluids. At the macroscopic level, the porous material is described by the Biot model defined in terms of the…

Optimization and Control · Mathematics 2018-12-03 Daniel Hübner , Eduard Rohan , Vladimír Lukeš , Michael Stingl

A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and…

Optimization and Control · Mathematics 2021-10-12 Harald Garcke , Paul Hüttl , Patrik Knopf

The design of irregular planar phased arrays (PAs) characterized by a highly-modular architecture is addressed. By exploiting the property of self-replicating tile shapes, also known as rep-tiles, the arising array layouts consist of tiles…

Signal Processing · Electrical Eng. & Systems 2023-04-19 Nicola Anselmi , Luca Tosi , Paolo Rocca , Giovanni Toso , Andrea Massa

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

We propose a novel approach to optimize the design of heterogeneous materials, with the goal of enhancing their effective fracture toughness under mode-I loading. The method employs a Gaussian processes-based Bayesian optimization framework…

Optimization and Control · Mathematics 2023-03-29 Sukhminder Singh , Lukas Pflug , Julia Mergheim , Michael Stingl