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Selecting the optimal material for a part designed through topology optimization is a complex problem. The shape and properties of the Pareto front plays an important role in this selection. In this paper we show that the compliance-volume…

Optimization and Control · Mathematics 2022-11-29 Edouard Duriez , Miguel Charlotte , Catherine Azzaro-Pantel , Joseph Morlier

Complex shapes are widely used to design products in several industries such as aeronautics, automotive and domestic appliances. Several variations of their curvatures and orientations generate difficulties during their manufacturing or the…

Other Computer Science · Computer Science 2012-07-03 Laurent Tapie , Kwamiwi Mawussi , Alain Bernard

This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…

Optimization and Control · Mathematics 2023-05-03 Harald Garcke , Kei Fong Lam , Robert Nürnberg , Andrea Signori

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

We discuss a topology optimization problem for an elastoplastic medium. The distribution of material in a region is optimized with respect to a given target functional taking into account compliance. The incremental elastoplastic problem…

Optimization and Control · Mathematics 2020-11-02 Stefano Almi , Ulisse Stefanelli

An additive manufacturing (AM) process often produces a {\it near-net} shape that closely conforms to the intended design to be manufactured. It sometimes contains additional support structure (also called scaffolding), which has to be…

Computational Geometry · Computer Science 2019-05-30 Saigopal Nelaturi , Morad Behandish , Amir M. Mirzendehdel , Johan de Kleer

The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…

Optimization and Control · Mathematics 2016-12-14 Igor Ostanin , Ivan Tsybulin , Mikhail Litsarev , Ivan Oseledets , Denis Zorin

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded…

Machine Learning · Computer Science 2025-10-29 Amin Heyrani Nobari , Lyle Regenwetter , Cyril Picard , Ligong Han , Faez Ahmed

This paper presents a density-based topology optimization approach to design structures under self-weight load. Such loads change their magnitude and/or location as the topology optimization advances and pose several unique challenges,…

Computational Engineering, Finance, and Science · Computer Science 2022-04-26 Prabhat Kumar

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

Structural optimization (topology, shapes, sizing) is an important tool for facilitating the emergence of new concepts in structural design. Normally, topology optimization is carried out at the early stage of design and then shape and…

Optimization and Control · Mathematics 2021-03-16 Ghislain Raze , Joseph Morlier

This paper firstly presents an implementation of multi-material topology optimization (MTO) for in-plane bi-directional functionally graded (IBFG) non-uniform thickness Reissner-Mindlin plates. The mathematical formulation of the MTO is…

Numerical Analysis · Mathematics 2023-09-29 Nam G. Luu , Thanh T. Banh

Moving Morphable Component (MMC) based topology optimization approach is an explicit algorithm since the boundary of the entity explicitly described by its functions. Compared with other pixel or node point-based algorithms, it is optimized…

Numerical Analysis · Mathematics 2019-10-17 Xinchao Jiang , Hu Wang , Yu Li , Kangjia Mo

Sim-to-real transfer remains a significant challenge in soft robotics due to the unpredictability introduced by common manufacturing processes such as 3D printing and molding. These processes often result in deviations from simulated…

Hybrid manufacturing (HM) technologies combine additive and subtractive manufacturing (AM/SM) capabilities in multi-modal process plans that leverage the strengths of each. Despite the growing interest in HM technologies, software tools for…

Computational Geometry · Computer Science 2022-06-06 George P. Harabin , Morad Behandish

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

Machine learning (ML) has been increasingly used for topology optimization (TO). However, most existing ML-based approaches focus on simplified benchmark problems due to their high computational cost, spectral bias, and difficulty in…

Machine Learning · Computer Science 2026-02-23 Xiangyu Sun , Shirin Hosseinmardi , Amin Yousefpour , Ramin Bostanabad

In this paper, a compact and efficient code implementation is presented for isogeometric topology optimization (ITO) approach. With the aid of B\.ezier extraction technique, a derived explicit stiffness matrix computation formula is applied…

Computational Engineering, Finance, and Science · Computer Science 2025-04-14 Xianda Xie , Zhihui Ou , Aodi Yang , Xiaobing Li , Shuting Wang

With the emergence of new photonic and plasmonic materials with optimized properties as well as advanced nanofabrication techniques, nanophotonic devices are now capable of providing solutions to global challenges in energy conversion,…

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

Machine Learning · Computer Science 2025-10-31 Di Zhang