{"title":"Exact treatment of volume constraint for RDE-based topology optimization of elastoplastic structures","authors":"","doi":"10.1016/j.enganabound.2024.105888","DOIUrl":null,"url":null,"abstract":"<div><p>For the reaction–diffusion equation (RDE) based topology optimization of elastoplastic structure, exactness in volume constraint can be crucial. As a non-traditional numerical method, the recently proposed exact volume constraint requires iterations to determine the precise Lagrangian multiplier. Conversely, conventional inexact volume constraint methods resemble a time-forward scheme, potentially leading to convergence issues. An approximate topological derivative for the 2D elastoplastic problem is derived and utilized to investigate the difference between employing exact and inexact volume constraint methods. A comprehensive examination is conducted by varying parameters such as mesh density, design domain aspect ratio, applied load, constrained volume ratio, and the diffusion coefficient <span><math><mi>τ</mi></math></span>. Results indicate that the inexactness of volume constraint can lead to more severe issues in elastoplasticity compared to elasticity. The exact volume constraint method not only yields significantly improved convergence in structural optimization but also reduces structural compliance and computational runtime. There might be speculation that the fluctuation caused by the traditional inexact treatment of volume constraints could prevent the optimization process from being trapped in a local minimum. However, contrary to this assumption, in elastoplastic cases, it often has the opposite effect, frequently driving the structure away from a global optimum. Particularly noteworthy is the observation that inexact volume constraint quite often results in very poor structures with exceedingly high compliance. On the other hand, increasing the normalization parameter can lead to substantial improvements in results. These findings underscore the necessity of exact volume constraint for nonlinear topology optimization problems.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":null,"pages":null},"PeriodicalIF":4.2000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S095579972400362X/pdfft?md5=97fb0a818116331a606a1a7da64cb5bd&pid=1-s2.0-S095579972400362X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S095579972400362X","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
For the reaction–diffusion equation (RDE) based topology optimization of elastoplastic structure, exactness in volume constraint can be crucial. As a non-traditional numerical method, the recently proposed exact volume constraint requires iterations to determine the precise Lagrangian multiplier. Conversely, conventional inexact volume constraint methods resemble a time-forward scheme, potentially leading to convergence issues. An approximate topological derivative for the 2D elastoplastic problem is derived and utilized to investigate the difference between employing exact and inexact volume constraint methods. A comprehensive examination is conducted by varying parameters such as mesh density, design domain aspect ratio, applied load, constrained volume ratio, and the diffusion coefficient . Results indicate that the inexactness of volume constraint can lead to more severe issues in elastoplasticity compared to elasticity. The exact volume constraint method not only yields significantly improved convergence in structural optimization but also reduces structural compliance and computational runtime. There might be speculation that the fluctuation caused by the traditional inexact treatment of volume constraints could prevent the optimization process from being trapped in a local minimum. However, contrary to this assumption, in elastoplastic cases, it often has the opposite effect, frequently driving the structure away from a global optimum. Particularly noteworthy is the observation that inexact volume constraint quite often results in very poor structures with exceedingly high compliance. On the other hand, increasing the normalization parameter can lead to substantial improvements in results. These findings underscore the necessity of exact volume constraint for nonlinear topology optimization problems.
期刊介绍:
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.