Article
Mechanics
Hui Liu, Lianxiong Chen, Tielin Shi, Qi Xia
Summary: In this paper, a novel approach is developed for optimizing the layout and shape of stiffeners based on the Mindlin plate theory. The layout and shape of stiffeners can be controlled by adjusting the design variables, and the coordinate mapping technique and high-order polynomial interpolation technique allow for more complex geometries. Numerical examples demonstrate the effectiveness of the proposed approach.
COMPOSITE STRUCTURES
(2022)
Article
Engineering, Multidisciplinary
Zeshang Li, Lei Wang, Geng Xinyu
Summary: With the diversification of engineering structure performance requirements and the continuous development of structural design refinement, structural design methods are facing more and more factors to be considered. This paper proposes a sensitivity mapping technique for topology optimization based on a gradient optimization algorithm and considers the influence of multi-source uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Computer Science, Interdisciplinary Applications
Ali Azari Nejat, Alexander Held, Niklas Trekel, Robert Seifried
Summary: This study proposes an efficient and stable topology optimization algorithm for slender structures by modifying the pseudo-time step size and Lagrange multiplier to replace unacceptable designs, adjusting the normal velocity formulation to avoid instabilities, and adding filtering-like adaptation terms to achieve smoother optimization convergence.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
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
Mechanics
Ying Zhou, Hao Li, Xiaopeng Li, Liang Gao
Summary: This paper presents a systematic optimization design method for multiphase auxetic metamaterials with different deformation mechanisms in both 2D and 3D scenarios. The method utilizes the parametric color level set (PCLS) to accurately describe the microstructures of different material phases and handles multiple material usage constraints efficiently. The design sensitivities are analyzed using the shape derivative theory, and the effective elasticity properties of multiphase composites are evaluated using the numerical homogenization method. Various symmetric conditions are imposed to induce re-entrant and chiral patterns in the metamaterials. The proposed method is demonstrated through numerical examples to tailor different types of multiphase auxetics.
COMPOSITE STRUCTURES
(2022)
Article
Engineering, Mechanical
Zhuo Huang, Ye Tian, Kang Yang, Tielin Shi, Qi Xia
Summary: A shape and generalized topology optimization method based on the level set-based density method is proposed for designing curved grid stiffeners. The method combines level set functions and basis functions to describe the overall layout and curvilinear path of the stiffeners, and uses interval projection to describe the width. The combination operation similar to Boolean operation union is achieved using the p-norm method. The proposed method is validated through numerical examples, demonstrating its effectiveness in changing the shape and topology of stiffeners during optimization.
JOURNAL OF MECHANICAL DESIGN
(2023)
Article
Engineering, Multidisciplinary
Mian Zhou, Mi Xiao, Yan Zhang, Jie Gao, Liang Gao
Summary: The proposed marching cubes-based isogeometric topology optimization method accurately describes structural boundaries and creates precise material description models, with the addition of relaxed topology derivatives to improve method robustness.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics, Applied
Son H. Nguyen, Tan N. Nguyen, Trung Nguyen-Thoi
Summary: This paper presents a stress-based topology optimization method for plate structures using a finite element level-set method. The method can resolve the singularity phenomenon arising in topology optimization under stress constraints without using any relaxation technique. The finite element method is used to solve the equations of design variables and the state and adjoint equations of plate structures with arbitrary complex geometries and boundaries.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Engineering, Multidisciplinary
Wei Sha, Mi Xiao, Liang Gao, Yan Zhang
Summary: This paper proposes a new level set based multi-material topology optimization method by developing a DS-MMLS model and implementing an alternating active-phase algorithm. The method can be easily extended to topology optimization problems with more material phases and shows significant effectiveness in numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Sandilya Kambampati, Hayoung Chung, H. Alicia Kim
Summary: This paper proposes a new methodology for computing boundary sensitivities in level set topology optimization using the discrete adjoint method. By combining local perturbations with derivatives of the objective function, boundary sensitivities can be calculated. This method avoids the smoothing or interpolation methods typically used in sensitivity calculations, improving accuracy and convergence characteristics.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Yang Liu, Cheng Yang, Peng Wei, Pingzhang Zhou, Jianbin Du
Summary: This paper discusses a new topology optimization method that combines density-based method with level-set description for efficient structural optimization and topological variation. By using a material interpolation with penalty, the update information becomes more distinguished, leading to stable convergence into solid-void solutions. The method is validated through benchmark examples in 2D and 3D, showing advantageous structural representations and better objective function values compared to the widely accepted SIMP method. Several numerical examples and MATLAB codes are provided to demonstrate the method's characteristics.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Chi Wu, Jianguang Fang, Shiwei Zhou, Zhongpu Zhang, Guangyong Sun, Grant P. Steven, Qing Li
Summary: The paper incorporates a phase-field damage model into the topology optimization framework to account for crack initiation and propagation in a path-dependent manner. The proposed approach enhances fracture resistance of structures made of brittle materials and introduces a path-dependent shape derivative to drive the optimization effectively. Three 2D benchmark examples and one 3D biomedical example are studied to demonstrate the effectiveness of the method in improving fracture resistance with more efficient use of materials and reducing stress concentration and fracture risks.
COMPUTERS & STRUCTURES
(2021)
Article
Engineering, Multidisciplinary
Xiaopeng Li, Liang Gao, Ying Zhou, Hao Li
Summary: The proposed hybrid level set method simultaneously optimizes supporting structure and embedded component positions and orientations. It represents components and supporting structure using explicit and implicit level sets, allowing for smooth geometries and clear interfaces. By using two sets of design variables in a unified optimization loop, the overall design variables are greatly reduced.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Hao Deng
Summary: This paper presents an efficient MATLAB code for the discrete adjoint-based level set method, which is suitable for 2D stress-constrained problems. The method advances the design boundaries using discrete adjoint sensitivities and allows for the application of general mathematical programming algorithms to handle multiple constraints.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Yi Lin, Weidong Zhu, Jiangxiong Li, Yinglin Ke
Summary: This paper proposes a level set method updated with finite difference scheme for structural topology optimization, using piecewise basis function interpolation for velocity field updating and avoiding the need for complicated upwind scheme and time-consuming reinitialization. Diffusion is introduced into the Hamilton-Jacobi equation, and a three-step splitting method is adopted to solve the equation, ensuring the numerical stability of the optimization process.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)