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
Engineering, Multidisciplinary
Nouman Saeed, Kai Long, Lixiao Li, Ayesha Saeed, Chengwan Zhang, Zhengkun Cheng
Summary: This article proposes an augmented Lagrangian-based topology optimization approach to minimize the volume fraction subject to multiple nodal displacement constraints. The method transforms the multiple constraint equations into an objective function and solves it through a series of unconstrained optimization problems. The study explains the theoretical aspects of the augmented Lagrangian approach and demonstrates its feasibility and reliability through numerical examples.
ENGINEERING OPTIMIZATION
(2023)
Article
Computer Science, Artificial Intelligence
Zhanhong Jiang, Chao Liu, Young M. Lee, Chinmay Hegde, Soumik Sarkar, Dongxiang Jiang
Summary: This paper introduces the Stochastic Augmented Lagrangian method (SALM) to address optimization problems in domain adaptation, finding optimal Lagrangian multipliers instead of manually selecting them. Experimental results show that SALM can find feasible points with arbitrary precision in domain adaptation problems with bounded penalty parameters, and approximate stationary infeasibility points with unbounded penalty parameters.
KNOWLEDGE-BASED SYSTEMS
(2022)
Article
Computer Science, Interdisciplinary Applications
Oliver Giraldo-Londono, Glaucio H. Paulino
Summary: PolyStress is a Matlab implementation for topology optimization with local stress constraints, which addresses linear and material nonlinear problems. The implementation is based on PolyTop and utilizes a Newton-Raphson scheme and an augmented Lagrangian method to solve nonlinear elasticity and stress-constrained problems consistently.
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
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
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
Mechanics
Hamid Reza Analooei, Mojtaba Azhari, Hamzeh Salehipour
Summary: In this study, thermo-electro-mechanical analysis of quadrilateral and triangular piezoelectric nanoplates was conducted using nonlocal theory and Kirchhoff plate theory. It was found that small-scale effect plays a significant role in the buckling and vibration behavior of piezoelectric nanoplates.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Computer Science, Artificial Intelligence
Maocan Song, Lin Cheng
Summary: With the increasing demand for travel and limited transportation resources, traffic congestion remains a challenging problem. This study considers the variability of travel times in vehicle routing optimization by utilizing historical travel time data. A mean-standard deviation based vehicle routing model is developed and solved using an augmented Lagrangian relaxation approach. The proposed method effectively reduces the relative gap between the lower and upper bounds in the solving procedure.
KNOWLEDGE-BASED SYSTEMS
(2022)
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
Engineering, Multidisciplinary
Yafeng Wang, Ole Sigmund
Summary: This study aims to optimize the buckling capacity of mechanical structures subjected to thermal and mechanical loading through a density-based topology optimization scheme. By decoupling the effects of mechanical and thermal loadings, the buckling aspects induced by each loading can be separately analyzed and optimized. The study also employs a multi-material topology optimization scheme to optimize the buckling capacity of active structures and prestressed structures.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
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
Automation & Control Systems
Necdet Serhat Aybat, Hesam Ahmadi, Uday V. Shanbhag
Summary: In this article, we discuss a first-order inexact augmented Lagrangian scheme for simultaneously learning the parameter theta* and computing the optimal solution x* in a misspecified optimization problem. Numerical results suggest that this scheme performs well in practice.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Computer Science, Interdisciplinary Applications
Anna Dalklint, Mathias Wallin, Daniel A. Tortorelli
Summary: This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. Through the use of nonlinear large deformation hyperelastic simulation, combined with Newton's method and eigenvalue analysis, as well as Helmholtz PDE-filter and method of moving asymptotes, the design optimization is successfully achieved, and the effectiveness of the method is validated through numerical examples.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Multidisciplinary
Jonathan B. Russ, Haim Waisman
Summary: A new formulation is proposed for incorporating local ductile failure constraints and buckling resistance into elastoplastic structural design efficiently and robustly. An aggregate objective function is constructed to maximize the total work in an elastoplastic analysis and to include load factors from a separate linear elastic buckling analysis. The suggested framework significantly improves structural responses such as peak load carrying capacity and total external work required to reach the peak load.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
