Article
Computer Science, Interdisciplinary Applications
Oliver Giraldo-Londono, Miguel A. Aguilo, Glaucio H. Paulino
Summary: The approach is based on an augmented Lagrangian method, effectively solving stress-constrained topology optimization problems for structures subjected to general dynamic loading. Normalizing the penalty term and penalizing constraints associated with high stress values more severely are key strategies employed for handling problems with a large number of stress constraints.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Multidisciplinary
Gustavo Assis da Silva, Niels Aage, Andre Teofilo Beck, Ole Sigmund
Summary: This research compares local and global stress constraint strategies in topology optimization and finds that local strategies are less sensitive to the continuation procedure, leading to better quality results with fewer iterations compared to global strategies. It is also discovered that global strategies become competitive when using P values larger than 100, but require a slow continuation procedure. The local strategies based on the augmented Lagrangian method provide the best compromise between computational cost and performance.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Vaishnavi Kale, Niels Aage, Marc Secanell
Summary: This article explores the importance of flywheel energy storage systems in grid energy storage applications and presents a multi-objective formulation to enhance energy capacity and reduce weight. By utilizing stress-constrained topology optimization and local stress constraints, improved designs with better performance can be achieved.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Chemistry, Physical
Kai Long, Zhuo Chen, Chengwan Zhang, Xiaoyu Yang, Nouman Saeed
Summary: The paper proposes a methodology on the topological design of porous structure, transforming the primary optimization problem with bounds of local volume constraints into unconstrained programming through a series of minimization sub-problems. The effectiveness of the proposed approach is illustrated through numerical tests, and the impacts of various factors on the final designs are investigated.
Article
Engineering, Multidisciplinary
Gustavo Assis da Silva, Niels Aage, Andre Teofilo Beck, Ole Sigmund
Summary: This article introduces a three-dimensional design methodology that addresses the limitations of stress constraints in topology optimization, proving the necessity of robust formulations in handling manufacturing uncertainty. Numerical investigations demonstrate the effectiveness of the approach in solving very large-scale problems with hundreds of millions of stress constraints.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Oliver Giraldo-Londono, Jonathan B. Russ, Miguel A. Aguilo, Glaucio H. Paulino
Summary: This study presents a formulation for topology optimization of structures with constraints on the first principal stress, solved using the augmented Lagrangian method to consider local stress constraints. Numerical examples demonstrate the effectiveness of the framework for practical problems with numerous local constraints, such as the three-dimensional antenna support bracket with over one million constraints.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Mathematics
Xiaoyan Teng, Can Wang, Xudong Jiang, Xiangyang Chen
Summary: Topology optimization is an effective design strategy for improving the fatigue resistance of engineering structures. However, the direct calculation of large-scale local fatigue constraints is challenging due to high computational cost. In this study, an augmented Lagrangian scheme is used to accurately meet the local fatigue constraints and reduce the number of constraints. The proposed approach, which retains the local nature of fatigue constraints, achieves higher fatigue resistance to material consumption ratio compared to the traditional P-norm method.
Article
Computer Science, Interdisciplinary Applications
Tao Xu, Xiaoshan Lin, Yi Min Xie
Summary: A novel topology optimization method based on the bi-directional evolutionary structural optimization (BESO) method is proposed in this study to increase buckling resistance in structural design. The method uses only two discrete statuses for design variables to alleviate numerical issues associated with pseudo buckling modes. Multiple buckling constraints are aggregated into a differentiable one using the Kreisselmeier-Steinhauser aggregation function. The developed optimization algorithm with buckling constraints significantly improves structural stability with a slight increase in compliance, as shown in numerical results.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Automation & Control Systems
Martin P. Neuenhofen, Eric C. Kerrigan
Summary: We propose a modified augmented Lagrangian method (ALM) to minimize constrained optimization problems with large quadratic penalties of inconsistent equality constraints. This modification addresses the issue of ALM's failure to converge when the equality constraints are inconsistent. The modified ALM demonstrates faster convergence in minimizing certain quadratic penalty augmented functions compared to the quadratic penalty method (QPM).
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Automation & Control Systems
Alessandro Falsone, Maria Prandini
Summary: This paper proposes a novel Augmented Lagrangian Tracking distributed optimization algorithm for solving multi-agent optimization problems. The algorithm features a constant penalty parameter, the ability to cope with unbounded local constraint sets, and the ability to handle both affine equality and nonlinear inequality coupling constraints.
Article
Computer Science, Interdisciplinary Applications
Xiaoya Zhai, Falai Chen, Jun Wu
Summary: This paper introduces a method of treating stresses as optimization variables using an augmented Lagrangian formulation. The effectiveness and efficiency of this approach are demonstrated through simple truss examples and various continuum structure optimization settings.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Zhuo Chen, Kai Long, Chengwan Zhang, Xiaoyu Yang, Feiyu Lu, Rixin Wang, Benliang Zhu, Xianmin Zhang
Summary: This paper proposes a novel methodology for fatigue-resistance topology optimization considering general loads. The independent rainflow counting method is utilized for structural damage estimation, and a damage penalization model is adopted to reduce nonlinearity. Numerical tests validate the effectiveness of the proposed method and further investigation is conducted into the influences of general loads, damage penalization model, and manufacturing error robustness.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Mathematics, Applied
Jinshan Zeng, Wotao Yin, Ding-Xuan Zhou
Summary: The augmented Lagrangian method (ALM) is a useful method for constrained optimization, but it can experience oscillations and divergence when the underlying problem is nonconvex and nonsmooth. This paper modifies ALM to use a Moreau envelope and establishes its convergence. Two practical variants are also proposed.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Federico Ferrari, Ole Sigmund, James K. Guest
Summary: The Matlab code presented here is designed for topology optimization based on linearized buckling criteria, handling multiple objectives or constraints efficiently. By using aggregation functions, sequential approximation, and vectorized implementation, the code improves efficiency and reduces computational bottlenecks. This allows for solving buckling topology optimization problems of significant size on a laptop, demonstrating code flexibility and performance through structural design examples.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Mathematics, Applied
Lu Lu, Raphael Pestourie, Wenjie Yao, Zhicheng Wang, Francesc Verdugo, Steven G. Johnson
Summary: Inverse design, such as topology optimization, is widely used in engineering for achieving targeted properties by optimizing designed geometries. The proposed physics-informed neural networks with hard constraints (hPINNs) can effectively solve topology optimization problems without the need for a large dataset, demonstrating smoother design outcomes compared to conventional methods.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Engineering, Multidisciplinary
Habeun Choi, Heng Chi, Kyoungsoo Park, Glaucio H. Paulino
Summary: An adaptive mesh morphogenesis method is proposed for coarsening arbitrary unstructured meshes, utilizing a posteriori error estimation and an edge straightening scheme. The method can be recursively conducted, regardless of element type and mesh generation counting. Employing a topology-based data structure to handle mesh modification events, it effectively handles mesh coarsening for arbitrarily shaped elements while capturing problematic regions with sharp gradients or singularity.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Mechanics
Kyoungsoo Park, Heng Chi, Glaucio H. Paulino
Summary: A B-bar formulation of the virtual element method (VEM) is presented for analyzing both nearly incompressible and compressible materials, successfully removing locking behavior for nearly incompressible materials. The convergence and accuracy of the method are discussed using examples in 2D and 3D with various element shapes.
Article
Computer Science, Interdisciplinary Applications
Oliver Giraldo-Londono, Glaucio H. Paulino
Summary: The study introduces a Matlab implementation for topology optimization of structures under dynamic loads, using various methods and techniques to address structural dynamics problems and solve non-self-adjoint topology optimization problems. Several numerical examples are presented with detailed explanations and summarized in a benchmark problem library.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Chemistry, Multidisciplinary
Fernando Senhora, Emily D. Sanders, Glaucio H. Paulino
Summary: Spinodal architected materials optimize design of multiscale structures by varying spinodal class, orientation, and porosity, leading to efficient material placement along stress trajectories with enhanced mechanical and biological functions.
ADVANCED MATERIALS
(2022)
Article
Engineering, Mechanical
Fufu Yang, Miao Zhang, Jiayao Ma, Zhong You, Ying Yu, Yan Chen, Glaucio H. Paulino
Summary: Resch patterns are tessellation origami patterns consisting of more than one type of polygons. They are generally rigid foldable but have a large number of degrees of freedom. In order to achieve one-DOF forms of triangular Resch pattern units, the thick-panel technique is employed to replace spherical linkages with spatial linkages. The compatibility among all the vertices is studied by kinematic analysis, and two design schemes are obtained to form a one-DOF origami structure.
MECHANISM AND MACHINE THEORY
(2022)
Article
Multidisciplinary Sciences
Qiji Ze, Shuai Wu, Jun Nishikawa, Jize Dai, Yue Sun, Sophie Leanza, Cole Zemelka, Larissa S. Novelino, Glaucio H. Paulino, Ruike Renee Zhao
Summary: Researchers have developed a magnetically actuated small-scale origami crawler with inplane contraction, which can crawl and steer in confined spaces. This crawler has magnetically tunable structural stiffness, allowing it to overcome large resistances, and it has the ability to store and release drugs internally, demonstrating its multifunctionality.
Article
Engineering, Mechanical
Diego Misseroni, Phanisri P. Pratapa, Ke Liu, Glaucio H. Paulino
Summary: This study presents a novel experimental setup for studying the Poisson effects in 2D origami tessellations. The setup was used to measure the Poisson's ratio of the Morph, Miura-ori, and Eggbox patterns, and the results were consistent with theory and simulations. This experimental technique can be applied to investigate other tunable properties of origami metamaterials.
EXTREME MECHANICS LETTERS
(2022)
Article
Chemistry, Multidisciplinary
Ke Liu, Phanisri P. Pratapa, Diego Misseroni, Tomohiro Tachi, Glaucio H. Paulino
Summary: This research explores the geometrical-frustration-induced anisotropy and inhomogeneity to achieve unique properties of metamaterials. Using a triclinic metamaterial system based on a Trimorph origami pattern, a folding motion is created that results in an unusual Poisson effect and reversible auxeticity. Tessellating tristable unit cells produces phenomena resembling linear and point defects due to geometric frustration. This frustration can be reprogrammed into distinct stable and inhomogeneous states by selecting the location of point defects. These findings have potential applications in wave propagation control and compliant microrobots.
ADVANCED MATERIALS
(2022)
Article
Engineering, Multidisciplinary
Fernando V. Senhora, Heng Chi, Yuyu Zhang, Lucia Mirabella, Tsz Ling Elaine Tang, Glaucio H. Paulino
Summary: This article proposes an artificial intelligence approach to accelerate topology optimization, capturing the underlying physics of the problem. The framework demonstrates effectiveness and scalability through various design examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Multidisciplinary Sciences
James McInerney, Glaucio H. Paulino, D. Zeb Rocklin
Summary: This study develops a formalism to investigate the interplay between geometric symmetries and functionality in origami crease patterns. It reveals that the anticommuting symmetry defines a class of crease pattern geometries with equal and opposite Poisson's ratios.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Green & Sustainable Science & Technology
Xunhao Ding, Punyaslok Rath, Oliver Giraldo-Londono, William G. Buttlar, Tao Ma
Summary: This study investigates the effects of rubber on anti-crack resistance for binders at low temperatures using the Discrete Element Method. The simulation results show that rubber particles play a significant role in improving the binder's crack resistance, resulting in a ductile failure mode and higher fracture energy.
JOURNAL OF CLEANER PRODUCTION
(2022)
Article
Computer Science, Interdisciplinary Applications
Oliver Giraldo-Londono, Jonathan B. Russ, Miguel A. Aguilo, Glaucio H. Paulino
Summary: This study presents a formulation for topology optimization of structures with constraints on the first principal stress, solved using the augmented Lagrangian method to consider local stress constraints. Numerical examples demonstrate the effectiveness of the framework for practical problems with numerous local constraints, such as the three-dimensional antenna support bracket with over one million constraints.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Materials Science, Multidisciplinary
Jonathan B. Russ, Glaucio H. Paulino
Summary: In order to enhance structural resistance to material failure, numerous topology optimization formulations have been proposed. This research extends the former method by constraining local failure criteria in a manner inspired by typical gradient-enhanced damage models. The proposed formulation relies on linear physics during the optimization procedure, greatly increasing its speed and robustness. Additionally, the study investigates the size effect introduced by using a numerical model and provides select observations, such as spurious fin-like patterns that can emerge depending on the structure and loading conditions. Finally, the load capacity of each optimized design is verified through a post-optimization verification procedure unaffected by the design parameterization and material interpolation schemes.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Multidisciplinary Sciences
Fernando V. Senhora, Ivan F. M. Menezes, Glaucio H. Paulino
Summary: Topology optimization problems often focus on a single or a few discrete load cases, while practical structures are subjected to infinitely many load cases that vary in intensity, location, and direction. This study proposes a locally stress-constrained topology optimization method that considers continuously varying load directions to ensure structural integrity under more realistic loading conditions.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
