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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

We present a computational design methodology for topology optimization of multi-material-based flexoelectric composites. The methodology extends our recently proposed design methodology for a single flexoelectric material. We adopt the…

Computational Physics · Physics 2019-01-31 Hamid Ghasemi , Harold S. Park , Timon Rabczuk

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

Computational Engineering, Finance, and Science · Computer Science 2024-05-14 Gabriel Garayalde , Matteo Torzoni , Matteo Bruggi , Alberto Corigliano

In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks…

Computational Engineering, Finance, and Science · Computer Science 2017-06-13 Bo Zhu , Mélina Skouras , Desai Chen , Wojciech Matusik

In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set…

Computational Engineering, Finance, and Science · Computer Science 2023-07-19 Chuong Nguyen , Xiaoying Zhuang , Ludovic Chamoin , Hung Nguyen-Xuan , Xianzhong Zhao , Timon Rabczuk

This paper provides an extended level set (X-LS) based topology optimiza- tion method for multi material design. In the proposed method, each zero level set of a level set function {\phi}ij represents the boundary between materials i and j.…

Computational Engineering, Finance, and Science · Computer Science 2022-03-10 Masaki Noda , Yuki Noguchi , Takayuki Yamada

This paper provides an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The orientation angle optimization is based on a topological derivative, which measures the…

Computational Engineering, Finance, and Science · Computer Science 2023-06-21 Masaki Noda , Kei Matsushima , Takayuki Yamada

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

In this paper we study the problem of the optimal distribution of two materials on smooth submanifolds $M$ of dimension $d-1$ in $\mathbf R^d$ without boundary by means of the topological derivative. We consider a class of shape…

Optimization and Control · Mathematics 2026-04-01 Peter Gangl , Kevin Sturm

We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…

Computational Engineering, Finance, and Science · Computer Science 2025-05-27 Jonathan Stollberg , Tarun Gangwar , Oliver Weeger , Dominik Schillinger

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

We consider the topology optimization problem of a 2d permanent magnet synchronous machine in magnetostatic operation with demagnetization. This amounts to a PDE-constrained multi-material design optimization problem with an additional…

Optimization and Control · Mathematics 2024-04-19 Nepomuk Krenn , Peter Gangl

We propose a model-based, automated, bottom-up approach for design, which is applicable to various physical domains, but in this work we focus on the electrical domain. This bottom-up approach is based on a meta-topology in which each link…

Optimization and Control · Mathematics 2023-02-17 Ion Matei , Maksym Zhenirovskyy , John Maxwell , Johan de Kleer

We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is…

Optimization and Control · Mathematics 2026-04-01 Peter Gangl , Michael H. Gfrerer

Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…

Numerical Analysis · Mathematics 2026-04-01 Peter Gangl , Nico Nees , Michael Stingl

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

This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…

Optimization and Control · Mathematics 2017-01-24 Matthew Lawry , Kurt Maute

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…

Computational Engineering, Finance, and Science · Computer Science 2020-05-20 Reza Behrou , Maroun Abi Ghanem , Brianna C. Macnider , Vimarsh Verma , Ryan Alvey , Jinho Hong , Ashley F. Emery , Hyunsun Alicia Kim , Nicholas Boechler

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

This paper presents a structural optimisation method in three-dimensional acoustic-elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed…

Numerical Analysis · Mathematics 2016-12-21 Hiroshi Isakari , Toyohiro Kondo , Toru Takahashi , Toshiro Matsumoto
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