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This paper presents a topology optimization framework for structural problems subjected to transient loading. The mechanical model assumes a linear elastic isotropic material, infinitesimal strains, and a dynamic response. The optimization…

Classical Physics · Physics 2017-05-05 Reza Behrou , James K. Guest

Topology optimization of microstructures plays a critical role in optimizing functional performance across diverse engineering applications. While metamaterials with enhanced mechanical properties -- such as hyperelasticity, energy…

Soft Condensed Matter · Physics 2025-01-27 Weiming Wang , Yanhao Hou , Renbo Su , Weiguang Wang , Charlie C. L. Wang

This paper proposes a self-support topology optimization method that considers distortion to improve the manufacturability of additive manufacturing. First, a self-support constraint is proposed that combines an overhang angle constraint…

Computational Engineering, Finance, and Science · Computer Science 2022-12-15 Takao Miki

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

A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…

Optimization and Control · Mathematics 2012-05-01 Daniel P. Mohr , Ina Stein , Thomas Matzies , Christina A. Knapek

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

A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology…

Neural and Evolutionary Computing · Computer Science 2025-02-21 Hongrui Chen , Xingchen Liu , Levent Burak Kara

Aligning lattices based on local stress distribution is crucial for achieving exceptional structural stiffness. However, this aspect has primarily been investigated under a single load condition, where stress in 2D can be described by two…

Computational Engineering, Finance, and Science · Computer Science 2025-01-20 Junpeng Wang , Rüdiger Westermann , Xifeng Gao , Jun Wu

This paper presents a density-based topology optimization approach considering additive manufacturing limitations. The presented method considers the minimum size of parts, the minimum size of cavities, the inability of printing overhanging…

Computational Engineering, Finance, and Science · Computer Science 2022-04-18 Prabhat Kumar , Eduardo Fernández

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

We consider the shape and topology optimization problem to design a structure that minimizes a weighted sum of material consumption and (linearly) elastic compliance under a fixed given boundary load. As is well-known, this problem is in…

Optimization and Control · Mathematics 2022-06-22 Jonas Potthoff , Benedikt Wirth

In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…

Optimization and Control · Mathematics 2019-11-13 Fabio Botelho , Alexandre Molter

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

We present a novel de-homogenization approach for efficient design of high-resolution load-bearing structures. The proposed approach builds upon a streamline-based parametrization of the design domain, using a set of space-filling and…

Computational Engineering, Finance, and Science · Computer Science 2022-07-20 Junpeng Wang , Rüdiger Westermann , Jun Wu

Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…

Computational Engineering, Finance, and Science · Computer Science 2024-10-29 Anna Dalklint , Rasmus E. Christiansen , Ole Sigmund

Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is increasingly widely used in many fabrication applications to achieve a target deformation behavior…

Graphics · Computer Science 2024-07-25 Davi Colli Tozoni , Zizhou Huang , Daniele Panozzo , Denis Zorin

Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This task is known to be hard in general but tractable for a number…

Combinatorics · Mathematics 2026-03-17 Anthony Meunier , Lhouari Nourine , Simon Vilmin

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

The optimization of porous infill structures via local volume constraints has become a popular approach in topology optimization. In some design settings, however, the iterative optimization process converges only slowly, or not at all even…

Computational Engineering, Finance, and Science · Computer Science 2022-03-22 Junpeng Wang , Jun Wu , Rüdiger Westermann

The present paper introduces a hybrid explicit-implicit topology optimization method for shell-infill composite structure design. The proposed approach effectively combines the advantages of the explicit Moving Morphable Component (MMC)…

Optimization and Control · Mathematics 2024-03-26 Yilin Guo , Chang Liu , Xu Guo