Article
Mechanics
Jiantao Bai, Wenjie Zuo
Summary: This article proposes a level set topology optimization method to design coated structures with multiple infill materials. The method constructs a multi-material interpolation model by combining multiple level set functions and derives shape derivatives for the multi-material optimization model of the coated structures for the first time.
COMPOSITE STRUCTURES
(2022)
Article
Mathematics
Jianliang Chen, Qinghai Zhao, Liang Zhang
Summary: This paper introduces a multi-material topology optimization formulation for thermo-elastic structures, utilizing an ordered-SIMP multiple materials interpolation model and the adjoint variable method to achieve clear topologies for complicated material combinations and demonstrate sensitivity to temperature variations.
Article
Mathematics, Applied
Aiqun Huang
Summary: A proximal augmented method for solving semidefinite programs based on the Augmented Lagrangian method is introduced. The study focuses on theoretical properties and shows convergence under weaker conditions. Numerical results indicate the potential efficiency of the new method.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Kiarash Kashanian, Il Yong Kim
Summary: This study introduces a new method, CTMO, for simultaneous optimization of thickness and material selection in complex shell structures, aimed at practical applications. Through academic examples and design studies of aircraft wings, the effectiveness and feasibility of this method are demonstrated.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Mechanics
Dzenan Hozic, Carl-Johan Thore, Christopher Cameron, Mohamed Loukil
Summary: HFP introduces a novel way to parametrize candidate materials in optimization problems, using a filtering technique based on hyperbolic functions. Despite the additional non-linearity introduced, HFP has fewer optimization variables and constraints compared to DMTO and SFP, showing consistent performance in optimizing composite plates.
COMPOSITE STRUCTURES
(2021)
Article
Engineering, Multidisciplinary
Jiawei Tian, Manqi Li, Zhonghao Han, Yong Chen, Xianfeng David Gu, Q. J. Ge, Shikui Chen
Summary: By optimizing the material layout, topologically optimized designs of ferromagnetic soft active structures with flexible motion can be achieved. The reconciled level set method within the X-LSM framework is implemented for the first time to design multi-material ferromagnetic soft active structures on free-form surfaces.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Automation & Control Systems
Pedro Felzenszwalb, Caroline Klivans, Alice Paul
Summary: This article introduces a clustering method that uses a semidefinite programming relaxation of the Max k-Cut problem. The method is based on a new approach to rounding the solution of an SDP relaxation using iterated linear optimization. The experiments show that using fixed point iteration for rounding the Max k-Cut SDP relaxation yields significantly better results compared to randomized rounding.
JOURNAL OF MACHINE LEARNING RESEARCH
(2022)
Article
Mechanics
Jingyu Hu, Yunfeng Luo, Shutian Liu
Summary: This paper proposes a two-scale concurrent topology optimization method for structures composed of multiple lattice materials, optimizing the microstructures, topology, and material distribution concurrently while ensuring connections between different lattice materials. The method defines a multi-domain self-connected material interpolation model to describe macro-scale topology and interfaces between lattice materials accurately. By using the Solid Isotropic Material with Penalization interpolation and homogenization method, the proposed method effectively designs structures with superior mechanical properties.
COMPOSITE STRUCTURES
(2021)
Article
Mathematics, Applied
Yifei Wang, Kangkang Deng, Haoyang Liu, Zaiwen Wen
Summary: We propose a decomposition method based on the augmented Lagrangian framework to solve a wide range of semidefinite programming problems. The method can handle nonlinear objective functions, nonsmooth regularization, and general linear equality/inequality constraints. By using matrix factorization, the positive semidefinite variable and a group of linear constraints can be transformed into a variable on a smooth manifold. Theoretical analysis shows that the necessary optimality conditions for the factorized subproblem are also sufficient for the original subproblem under certain conditions. Extensive numerical experiments demonstrate the superiority of our proposed method compared to other state-of-the-art methods for large-scale semidefinite programming problems.
SIAM JOURNAL ON OPTIMIZATION
(2023)
Article
Mechanics
Xingjun Gao, Weihua Chen, Yingxiong Li, Gongfa Chen
Summary: This paper proposes an efficient method for robust multimaterial topology optimization problems of continuum structures under load uncertainty. The method minimizes the weighted sum of the mean and standard deviation of structural compliance for each material phase, separates the Monte Carlo sampling from the topology optimization procedure, and establishes an efficient procedure for sensitivity analysis. By using an alternating active-phase algorithm of the Gauss-Seidel version, the multi-material topology optimization problem is split into a series of binary topology optimization sub-problems, leading to the demonstration of the effectiveness of the proposed method through several 2D examples.
COMPOSITE STRUCTURES
(2021)
Article
Mechanics
M. R. Costa, A. Sohouli, A. Suleman
Summary: This study presents a computationally efficient topology optimization approach for lattice structures, while increasing design flexibility. The proposed two-scale concurrent optimization method achieves optimal topologies by simultaneously optimizing the macro-scale structure and the underlying material micro-structures. Surrogate models and an energy-based homogenization method combined with voxelization are used to represent material and geometrical properties. The optimized graded lattice structure outperforms the uniform lattice structure in terms of performance.
COMPOSITE STRUCTURES
(2022)
Article
Computer Science, Interdisciplinary Applications
Masatoshi Shimoda, Hirotaka Nakayama, Shota Suzaki, Ryo Tsutsumi
Summary: This paper proposes a simultaneous shape and topology optimization method for designing multi-material structures. The method effectively combines shape and topology optimization by using shape along with fictitious homogenized-density variations as design variables. The proposed method allows for obtaining an optimal multi-material laminated shell structure without the need for design parameterization, eliminating numerical instabilities such as checkerboard pattern and zigzag shape problems.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Multidisciplinary
Baoshou Liu, Xiaodong Huang, Yinan Cui
Summary: The rapid development of additive manufacturing provides new opportunities for fabricating multi-material structures. However, the graded-interface assumption between different materials often poses challenges in topology optimization. This study proposes a new element-based topology optimization algorithm that explicitly considers interface types and allows precise control of interface width. Numerical examples demonstrate that the optimized designs using this method achieve lower compliance compared to traditional multi-material designs.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Marek Tyburec, Jan Zeman, Martin Kruzik, Didier Henrion
Summary: The study introduces a strategy to compute guaranteed globally optimal solutions using a nonlinear semidefinite programming formulation over a semi-algebraic feasible set. By employing the Lasserre moment-sum-of-squares hierarchy, a sequence of outer convex approximations converging to the optimal solution is generated. The Curto-Fialkow flat extension theorem is then used to extract globally optimal solutions.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Lei Tang, Tong Gao, Longlong Song, Chengqi Zhang, Weihong Zhang
Summary: This paper proposes a load allocation topology optimization approach to meet the design requirement of thermo-elastic structures in engineering practice. By introducing a load allocation constraint and using average displacement as the objective function, sensitivity analyses based on the adjoint method are conducted and combined with the gradient-based algorithm. Numerical examples demonstrate the effectiveness of the proposed approach, and comparisons with solutions of standard topology optimization highlight the coupling effect between the load allocation constraint and the temperature field.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Software Engineering
Chin Pang Ho, Michal Kocvara, Panos Parpas
Summary: Inspired by multigrid methods, multilevel optimization methods have been proposed to solve structured optimization problems with better performance, especially for large-scale models. However, so far there is no theoretical explanation for the impressive convergence properties of multilevel optimization methods.
OPTIMIZATION METHODS & SOFTWARE
(2022)
Article
Computer Science, Interdisciplinary Applications
Lukas Pflug, Niklas Bernhardt, Max Grieshammer, Michael Stingl
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2020)
Article
Computer Science, Software Engineering
Michal Kocvara
Summary: The decomposition of large matrix inequalities can reduce the problem size of semidefinite optimization problems and improve efficiency by introducing new matrix variables with rank one that can be replaced by vector variables. This approach leads to significant improvement in efficiency and has demonstrated linear growth in complexity in numerical examples. The connection to the standard theory of domain decomposition and the outcomes of discrete Steklov-Poincare operators further illustrate the benefits of this method.
MATHEMATICAL PROGRAMMING
(2021)
Article
Engineering, Multidisciplinary
Sukhminder Singh, Lukas Pflug, Michael Stingl
Summary: Advances in computational modeling of solid fracture have led to new possibilities for structural design optimization to enhance fracture properties. By introducing viscous regularization and local approximation of cohesive law, the issue of non-uniqueness in rate-independent structural problems is addressed, allowing for integration of fracture problems into material optimization framework.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Software Engineering
Bich Ngoc Vu, Fabian Wein, Michael Stingl
Summary: This study focuses on gradient-based optimization of cellular structures, proposing a method to generate geometric descriptions that are additively manufacturable in a two-scale setting. By analyzing the suitability of unit cells and conducting homogenization-based optimization, the performance of cellular components with isotropic and anisotropic micro-structures is discussed.
COMPUTER-AIDED DESIGN
(2021)
Article
Chemistry, Physical
Thomas Meincke, Johannes Walter, Lukas Pflug, Thaseem Thajudeen, Andreas Voelkl, Paola Cardenas Lopez, Maximilian J. Uttinger, Michael Stingl, Satoshi Watanabe, Wolfgang Peukert, Robin N. Klupp Taylor
Summary: Anisotropic nanoparticles with tunable optical properties are synthesized through electroless deposition of silver patches onto colloidal silica particles. New methods are needed to rapidly determine patch yield, thickness, and coverage for process optimization. A novel approach based on multiwavelength analytical ultracentrifugation is presented, allowing simultaneous hydrodynamic and spectroscopic characterization of patchy particles.
JOURNAL OF COLLOID AND INTERFACE SCIENCE
(2022)
Article
Operations Research & Management Science
Martina Kuchlbauer, Frauke Liers, Michael Stingl
Summary: This paper introduces an algorithm for convex mixed-integer nonlinear robust optimization problems. The algorithm achieves robust protection up to a certain precision and does not rely on the specific structure of the inner worst-case problem. By approximating the non-convex adversarial problem and solving it as a mixed-integer linear problem, the necessary assumptions can be met. The paper also proposes an adaptive bundle method and cutting planes to deal with the arising nonlinear subproblems, and proves the finite convergence of the outer approximation algorithm.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2022)
Article
Engineering, Multidisciplinary
Sukhminder Singh, Lukas Pflug, Julia Mergheim, Michael Stingl
Summary: Recent developments in computational modeling of fracture have led to possibilities in designing structures against failure. This article presents a stochastic optimization approach to maximize delamination resistance, which is less sensitive to small perturbations of the design and leads to a robust solution.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Nico Nees, Lukas Pflug, Benjamin Mann, Michael Stingl
Summary: This article introduces a new design optimization method for nanoparticles, which uses the discrete dipole approximation (DDA) to approximate the solution of Maxwell's equation. In this method, each dipole is assigned a material property from a given catalog until a local minimum for the chosen design objective is obtained. The design updates are computed using a separable model, which allows for more complex design spaces to be investigated compared to finite element based approaches.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Jannis Greifenstein, Eloise Letournel, Michael Stingl, Fabian Wein
Summary: We propose a feature-mapping topology optimization approach using piecewise linear splines to represent curved features. Our contribution aims to optimize structures made from variable angle continuous fiber-reinforced filaments. The proposed model ensures rigorous continuous differentiability and efficient analysis of the signed distance field to the spline. The geometric description and sensitivity analysis are developed analytically and mapped to a discretized pseudo-density field for finite element analysis.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Bich Ngoc Vu, Vladimir Lukes, Michael Stingl, Eduard Rohan
Summary: We present a new approach and algorithm for solving two-scale material optimization problems, specifically optimizing the behavior of a fluid-saturated porous medium. This approach is widely applicable to multiphysics problems and utilizes homogenization to establish the relationship between microconfigurations and the macroscopic mathematical model. The efficiency of the method is demonstrated through numerical experiments.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Daniel Huebner, Fabian Wein, Michael Stingl
Summary: In recent years, there has been increased interest in components with detailed structures due to advancements in manufacturing techniques. Our study focuses on the optimization of graded lattice structures to enhance both global and local buckling resistance. We propose a two-scale optimization method based on asymptotic homogenization and a worst-case model to address pure local buckling and improve overall stability. Numerical examples and validations demonstrate the effectiveness of our approach, and the limitations and advantages of the worst-case model are discussed.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Johannes Semmler, Michael Stingl
Summary: This article discusses the numerical simulation and optimization of the optical properties of mono-layered nano-particulate films, focusing on the haze factor. A hybrid numerical method is proposed, reducing computational complexity significantly and allowing for structural optimization studies. The method is versatile and can be applied to various structural optimization problems.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Mathematics
Dennis Adelhuette, Denis Assmann, Tatiana Gonzalez Grandon, Martin Gugat, Holger Heitsch, Rene Henrion, Frauke Liers, Sabrina Nitsche, Ruediger Schultz, Michael Stingl, David Wintergerst
Summary: This study focuses on optimization problems under uncertain conditions, including probabilistic constraints and robustness constraints. By addressing complex uncertain gas network optimization problems with joint probabilistic/robust constraints, the relevance and solution approaches of these problems are demonstrated.
VIETNAM JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Julian Valentin, Daniel Huebner, Michael Stingl, Dirk Pflueger
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2020)
