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Topology optimization under uncertainty (TOuU) often defines objectives and constraints by statistical moments of geometric and physical quantities of interest. Most traditional TOuU methods use gradient-based optimization algorithms and…

Optimization and Control · Mathematics 2019-11-05 Subhayan De , Jerrad Hampton , Kurt Maute , Alireza Doostan

This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…

Computational Engineering, Finance, and Science · Computer Science 2025-01-28 Nan Feng , Guodong Zhang , Kapil Khandelwal

In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…

Optimization and Control · Mathematics 2018-12-13 Jannis Greifenstein , Michael Stingl

As the capabilities of additive manufacturing techniques increase, topology optimization provides a promising approach to design geometrically sophisticated structures which can be directly manufactured. Traditional topology optimization…

Optimization and Control · Mathematics 2014-01-28 Carlos H. Villanueva , Kurt Maute

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

This paper applies topology optimisation to the design of structures with periodic microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all…

Computational Engineering, Finance, and Science · Computer Science 2015-08-19 Joe Alexandersen , Boyan S. Lazarov

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

Aerodynamic optimization is ubiquitous in the design of most engineering systems interacting with fluids. A common approach is to optimize a performance function defined by a choice of an aerodynamic model, e.g., turbulence RANS model, and…

Optimization and Control · Mathematics 2021-05-04 Lluís Jofre , Alireza Doostan

Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…

Materials Science · Physics 2024-08-28 Harikrishnan Vijayakumaran , Jonathan B. Russ , Glaucio H. Paulino , Miguel A. Bessa

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

Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…

Analysis of PDEs · Mathematics 2023-07-10 Stefano Almi , Ulisse Stefanelli

Micro-structured materials consisting of an array of microstructures are engineered to provide the specific material properties. This present work investigates the design of cellular materials under the framework of level set, so as to…

Computational Engineering, Finance, and Science · Computer Science 2018-11-13 Jie Gao , Hao Li , Zhen Luo , Liang Gao , Peigen Li

Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…

Optimization and Control · Mathematics 2024-03-01 Alfredo Vitorino , Francisco A. M. Gomes

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

Topology optimization under uncertainty or reliability-based topology optimization is usually numerically very expensive. This is mainly due to the fact that an accurate evaluation of the probabilistic model requires the system to be…

Optimization and Control · Mathematics 2024-10-28 Lukas Pflug , Michael Stingl , Andrian Uihlein

To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…

Applied Physics · Physics 2026-04-07 Hongxin Wang , Jie Liu , Guilin Wen

This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes…

Optimization and Control · Mathematics 2021-07-27 Subhayan De , Kurt Maute , Alireza Doostan

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…

Statistical Mechanics · Physics 2017-09-13 Lester O. Hedges , H. Alicia Kim , Robert L. Jack

We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can…

Optimization and Control · Mathematics 2020-06-24 Peter Gangl

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
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