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An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…

Numerical Analysis · Mathematics 2018-06-27 Jorgen S. Dokken , Simon W. Funke , August Johansson , Stephan Schmidt

The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…

Machine Learning · Computer Science 2023-02-22 Jan N. Fuhg , Craig M. Hamel , Kyle Johnson , Reese Jones , Nikolaos Bouklas

Mechanical stresses are increasingly found to be associated with various biological functionalities. At the same time, topological defects are being identified across a diverse range of biological systems and are points of localized…

Soft Condensed Matter · Physics 2023-12-08 Lasse Bonn , Aleksandra Ardaševa , Amin Doostmohammadi

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

The layering approach used in fused filament fabrication (FFF) enables creation of complex designs generated by topology optimization. Defects associated with the layer-by-layer process, introduce considerable random variability to the…

Materials Science · Physics 2024-09-04 Zahra Kazemi , Craig A. Steeves

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

We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order…

Other Condensed Matter · Physics 2022-05-31 Bastian Telgen , Ole Sigmund , Dennis M. Kochmann

The paper presents an innovative methodology based on the use of a new predictive algorithm created by the researchers capable of obtaining the elastic modulus of a plastic material manufactured with MEX and its mechanical behaviour in the…

Computational Engineering, Finance, and Science · Computer Science 2025-08-20 J. M. Mercado Colmenero , C. Martin Donate

We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…

Numerical Analysis · Mathematics 2026-02-26 Vladimír Lukeš , Eduard Rohan

We present an $hr$-adaptivity framework for optimization of high-order meshes. This work extends the $r$-adaptivity method for mesh optimization by Dobrev et al., where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize…

Numerical Analysis · Mathematics 2022-05-25 Veselin Dobrev , Patrick Knupp , Tzanio Kolev , Ketan Mittal , Vladimir Tomov

We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently…

Computational Engineering, Finance, and Science · Computer Science 2025-12-09 Hagen Holthusen , Ellen Kuhl

This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…

Optimization and Control · Mathematics 2020-04-22 Shanglong Zhang , Arun L. Gain , Julian A. Norato

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

In this paper a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions…

Optimization and Control · Mathematics 2019-07-16 Ferdinando Auricchio , Elena Bonetti , Massimo Carraturo , Dietmar Hömberg , Alessandro Reali , Elisabetta Rocca

Topology optimization (TO) can be viewed as seeking an optimal solution in the design space of a given TO problem. For weakly non-linear TO problems, e.g., compliance minimization, sensitivity-based methods typically converge well, whereas…

Optimization and Control · Mathematics 2026-03-25 Ziliang Wang , Jiahua Wu , Jun Yang , Shintaro Yamasaki

Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for…

This work presents a multilevel approach to large--scale topology optimization accounting for linearized buckling criteria. The method relies on the use of preconditioned iterative solvers for all the systems involved in the linear buckling…

Numerical Analysis · Mathematics 2020-03-03 Federico Ferrari , Ole Sigmund

Although stress-constrained topology optimization has been extensively studied in structural design, the development of optimization frameworks to enable the creation of metamaterials with optimal mechanical performance is still an open…

Computational Engineering, Finance, and Science · Computer Science 2026-02-24 Yanda Chen , Sebastian Rodriguez , Beatriz Moya , Francisco Chinesta

Rigid link flapping mechanisms remain the most practical choice for flapping wing micro-aerial vehicles (MAVs) to carry useful payloads and onboard batteries for free flight due to their long-term durability and reliability. However, MAVs…

Robotics · Computer Science 2025-09-25 Shyam Sunder Nishad , Anupam Saxena

This study presents an automated topology optimization framework for designing pentamode acoustic metamaterials. It provides precise control over the material effective acoustic properties while minimizing the shear modulus to achieve…

Applied Physics · Physics 2026-03-03 Sebastiano Cominelli , Matteo Pozzi , Francesco Braghin
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