Article
Engineering, Multidisciplinary
Xianda Xie, Aodi Yang, Ning Jiang, Shuting Wang
Summary: The proposed topology optimization method using fully adaptive truncated hierarchical B-splines (ATHB-TO) successfully provides identical optimized designs at a lower computational burden and improved convergence rate. The adaptive mark strategy enhances computational efficiency and structural performance, outperforming TO performed on uniformly refined meshes.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Engineering, Multidisciplinary
Philip Luke Karuthedath, Abhinav Gupta, Bhagath Mamindlapelly, Rajib Chowdhury
Summary: This study proposes a continuous density-field based isogeometric topology optimization method using Polynomial splines over Hierarchical T-meshes (PHT-Splines). The method achieves a very smooth topology and adaptive mesh refinement through the control points and spline basis functions. It can import complex geometry and maintain geometrical and computational accuracy. The proposed method reduces Degree's-of-Freedom (DoF) requirement and achieves a significant reduction in DoF compared to existing methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Xianda Xie, Aodi Yang, Yingjun Wang, Ning Jiang, Shuting Wang
Summary: This study presents a fully adaptive isogeometric topology optimization method using moving morphable components through truncated hierarchical B-splines. It achieves local refinement and coarsening simultaneously during topology optimization, showing improved convergence rate and decreased computational burden. The approach successfully maximizes structural stiffness in two-dimensional and three-dimensional problems, demonstrating an effective MMC-based topology optimization method.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Multidisciplinary
Abhinav Gupta, Bhagath Mamindlapelly, Philip Luke Karuthedath, Rajib Chowdhury, Anupam Chakrabarti
Summary: This paper presents a novel adaptive isogeometric topology optimization methodology using the Geometry Independent Field approximaTion (GIFT) framework for Polynomial splines over Hierarchical T-meshes (PHT)-splines. The approach has merits such as the ability to construct complex geometries, computational gains, and avoidance of geometric errors.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Zeyang Feng, Qinglin Duan, Songtao Chen
Summary: This paper presents an efficient and robust approach in the framework of the finite element method for numerical analysis of crack problems. The discontinuity due to the presence of cracks is described by the technique of phantom nodes. The idea of introducing adaptive mesh refinement along with crack extension into the original phantom node method is presented.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Computer Science, Interdisciplinary Applications
Son H. Nguyen, Dongwoo Sohn, Hyun-Gyu Kim
Summary: This paper presents a new computational strategy for stress-constrained shape and topology optimization using level-set-based trimmed meshes. The proposed hr-adaptive mesh refinement scheme greatly reduces the computational cost and achieves a clear and explicit representation of desired optimal designs with stress constraints.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Mathematics, Applied
Annalisa Buffa, Carlotta Giannelli
Summary: This paper serves as an addendum to two articles on adaptive isogeometric methods with hierarchical splines, proposing new Poincare estimates by extending the support of hierarchical B-splines to accommodate disconnected supports. The new estimates aim to address cases where the original estimates are not applicable due to disconnected supports.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Hao Li, Takayuki Yamada, Pierre Jolivet, Kozo Furuta, Tsuguo Kondoh, Kazuhiro Izui, Shinji Nishiwaki
Summary: The proposed framework is a parallel distributed and open-source framework for full-scale 3D structural topology optimization, which combines parallel computing and mesh adaption techniques using a reaction-diffusion equation based level-set method. The framework can be easily extended to design complex engineering products with optimized structures represented by high-resolution and clear boundaries.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2021)
Article
Mathematics, Applied
Cesare Bracco, Carlotta Giannelli, Mario Kapl, Rafael Vazquez
Summary: Isogeometric analysis is used to solve high order partial differential equations by leveraging the smoothness of splines. This paper focuses on adaptive isogeometric methods with hierarchical splines and extends the construction of C-1 isogeometric spline spaces to multi-patch planar domains. A refinement algorithm is developed to ensure the linear independence of hierarchical splines on suitable hierarchical multi-patch mesh configurations, and it has linear complexity. The performance of the adaptive method is tested by solving the Poisson and the biharmonic problems.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
Yadong Zeng, Anqing Xuan, Johannes Blaschke, Lian Shen
Summary: A unified adaptive level set framework for incompressible two-phase flows is developed using a multi-level collocated grid, along with synchronization operations and a multilevel re-initialization method. The framework shows good numerical implementation and mass conservation, successfully resolving various canonical problems. Additionally, efficiency and significant speedup are demonstrated in a three-dimensional dam breaking simulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Romain Janodet, Carlos Guillamon, Vincent Moureau, Renaud Mercier, Ghislain Lartigue, Pierre Benard, Thibaut Menard, Alain Berlemont
Summary: This article presents a parallel and robust strategy for simulating turbulent incompressible two-phase flows on unstructured grids in complex geometries. The combination of a narrow-band accurate conservative level set/ghost-fluid framework with isotropic adaptive mesh refinement allows for accurate capture of interface dynamics and topology. The method has been validated through various tests and examples, demonstrating its spatial convergence, robustness, and efficiency. It also showcases the computational advantages of adaptive mesh refinement for simulating complex turbulent flows with large density ratios.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
David Munoz, Jose Albelda, Juan Jose Rodenas, Enrique Nadal
Summary: The article discusses the advantages and disadvantages of the commonly used SIMP method in topology optimization, and proposes a method combining techniques to improve the performance of TO, including the use of two meshes, two h-adaptive mesh refinement strategies, and discretization error estimation based on energy norm.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Erin Kuci, Miche Jansen
Summary: This paper presents a level set-based framework for structural topology optimization with local elasto-plastic stress constraints. The proposed method takes advantage of an elasto-plastic material model to achieve more efficient structures under extreme loading scenarios. It uses the Augmented Lagrangian approach to reduce computational effort and combines the level set and density-based geometrical descriptions to allow for automated hole seeding.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Engineering, Multidisciplinary
Cesare Bracco, Durkbin Cho, Carlotta Giannelli, Rafael Vazquez
Summary: This paper introduces the construction of additive multilevel preconditioners, known as BPX preconditioners, for solving the linear system in isogeometric adaptive schemes with hierarchical B-splines. The locality of hierarchical spline functions is exploited to design efficient multilevel decompositions, reducing computational effort on each level. The condition number of the preconditioned system is shown to be bounded independently of the number of levels for suitably graded hierarchical meshes, with numerical examples validating theoretical results and performance.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mechanics
Aodi Yang, Shuting Wang, Nianmeng Luo, Xianda Xie, Tifan Xiong
Summary: A novel adaptive multi-material topology optimization method based on isogeometric analysis is proposed in this study, which improves the numerical accuracy and boundary quality of multi-material problems through adaptive marking strategy and graded constraint.
COMPOSITE STRUCTURES
(2022)
Article
Mathematics, Interdisciplinary Applications
L. Noel, M. Schmidt, K. Doble, J. A. Evans, K. Maute
Summary: This paper proposes an eXtended IsoGeometric Analysis (XIGA) approach for multi-material problems. The approach utilizes immersed boundary techniques and enrichment methods, as well as higher-order B-spline functions for geometry representation and analysis. Boundary and interface conditions are enforced weakly via Nitsche's method, and numerical instabilities are mitigated using a new stabilization methodology.
COMPUTATIONAL MECHANICS
(2022)