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This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…

Numerical Analysis · Mathematics 2024-01-08 Manaswinee Bezbaruah , Matthias Maier , Winnifried Wollner

We study the finite element approximation of the solid isotropic material with penalization method (SIMP) for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local…

Numerical Analysis · Mathematics 2024-11-21 Ioannis P. A. Papadopoulos

The traditional element-based topology optimization based on material penalization typically aims at a 0/1 design. Our numerical experiments reveal that the compliance of a smooth design is overestimated when material properties of boundary…

Computational Engineering, Finance, and Science · Computer Science 2020-06-09 Xiaodong Huang

We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid…

Computational Engineering, Finance, and Science · Computer Science 2021-05-21 Li Zheng , Siddhant Kumar , Dennis M. Kochmann

Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures, a novel asymptotic homogenisation topology optimisation…

Computational Engineering, Finance, and Science · Computer Science 2019-12-18 Dingchuan Xue , Yichao Zhu , Shaoshuai Li , Chang Liu , Weisheng Zhang , Xu Guo

This work presents a computational method for the design of architected truss lattice materials where each strut can be made of one of a set of available materials. We design the lattices to extremize effective properties. As customary in…

Computational Engineering, Finance, and Science · Computer Science 2020-04-22 Hesaneh Kazemi , Ashkan Vaziri , Julian A. Norato

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

This paper presents a computationally efficient method for the optimal design of silica aerogel porous material systems, balancing thermal insulation performance with mechanical stability under stress concentrations. The proposed approach…

Computational Engineering, Finance, and Science · Computer Science 2025-04-03 Pratyush Kumar Singh , Danial Faghihi

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

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

In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…

Computational Engineering, Finance, and Science · Computer Science 2023-07-06 Philipp Diercks , Karen Veroy , Annika Robens-Radermacher , Jörg F. Unger

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…

Optimization and Control · Mathematics 2024-04-18 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

Topology optimization (TO) has experienced a dramatic development over the last decades aided by the arising of metamaterials and additive manufacturing (AM) techniques, and it is intended to achieve the current and future challenges. In…

The objective of this study is to highlight the effect of porosity variation in a topology optimization process in the field of fluid dynamics. Usually a penalization term added to momentum equation provides to get material distribution.…

Fluid Dynamics · Physics 2020-04-23 Rakotobe Michaël , Ramalingom Delphine , Cocquet Pierre-Henri , Bastide Alain

We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…

Optimization and Control · Mathematics 2025-12-17 Yixin Tan , Fang Feng , Shengfeng Zhu

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

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

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 introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element…

Numerical Analysis · Mathematics 2019-05-21 Kosala Bandara , Fehmi Cirak

Multiply connected freeform surface features are widely encountered in industrial components, where toolpath generation often suffers from discontinuities, sharp turns, non-uniform scallop heights, and incomplete boundary coverage. This…

Robotics · Computer Science 2026-04-27 Shen Changqing , Xu Bingzhou , Qi Bosong , Zhang Xiaojian , Yan Sijie , Ding Han