{"title":"针对局部应力约束设计的等几何拓扑优化方法","authors":"Zhao Fan , Liang Gao , Hao Li","doi":"10.1016/j.compstruc.2024.107564","DOIUrl":null,"url":null,"abstract":"<div><div>Engineering structures are required to meet strength conditions to ensure engineering safety, where the maximum stress level of the structure mainly characterizes the structural strength. This study proposes an isogeometric topology optimization method for the local stress-constrained design. This method establishes an optimization model with volume fraction as the objective function and maximum von Mises stress as the constraint condition. The augmented lagrangian approach is introduced to ensure that the design results satisfy stress constraints locally. To increase the convergence rate of stress-constrained topology optimization, we develop a new stress constraint function, and compare it with the other two stress constraint functions proposed by previous research. Sensitivity analysis of the local stress-constraint and volume objective based on an isogeometric topology optimization framework is systematically derived. The design result is compared with the traditional global stress minimization design through typical numerical examples. In addition, this method is extended to the three-dimensional stress-constrained topology optimization design problem that has rarely been studied in the isogeometric-analysis-based topology optimization framework. Several typical numerical examples are presented to demonstrate the method’s effectiveness. It demonstrates that the proposed method inherits the merits of the exact geometry and high-order continuity between elements of isogeometric analysis and can effectively control the maximum von Mises stress level of structures, with a faster convergence rate.</div></div>","PeriodicalId":50626,"journal":{"name":"Computers & Structures","volume":"305 ","pages":"Article 107564"},"PeriodicalIF":4.4000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Isogeometric topology optimization method for design with local stress constraints\",\"authors\":\"Zhao Fan , Liang Gao , Hao Li\",\"doi\":\"10.1016/j.compstruc.2024.107564\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Engineering structures are required to meet strength conditions to ensure engineering safety, where the maximum stress level of the structure mainly characterizes the structural strength. This study proposes an isogeometric topology optimization method for the local stress-constrained design. This method establishes an optimization model with volume fraction as the objective function and maximum von Mises stress as the constraint condition. The augmented lagrangian approach is introduced to ensure that the design results satisfy stress constraints locally. To increase the convergence rate of stress-constrained topology optimization, we develop a new stress constraint function, and compare it with the other two stress constraint functions proposed by previous research. Sensitivity analysis of the local stress-constraint and volume objective based on an isogeometric topology optimization framework is systematically derived. The design result is compared with the traditional global stress minimization design through typical numerical examples. In addition, this method is extended to the three-dimensional stress-constrained topology optimization design problem that has rarely been studied in the isogeometric-analysis-based topology optimization framework. Several typical numerical examples are presented to demonstrate the method’s effectiveness. It demonstrates that the proposed method inherits the merits of the exact geometry and high-order continuity between elements of isogeometric analysis and can effectively control the maximum von Mises stress level of structures, with a faster convergence rate.</div></div>\",\"PeriodicalId\":50626,\"journal\":{\"name\":\"Computers & Structures\",\"volume\":\"305 \",\"pages\":\"Article 107564\"},\"PeriodicalIF\":4.4000,\"publicationDate\":\"2024-10-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers & Structures\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0045794924002931\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045794924002931","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
摘要
工程结构需要满足强度条件以确保工程安全,其中结构的最大应力水平主要表征结构强度。本研究提出了一种局部应力约束设计的等几何拓扑优化方法。该方法建立了一个以体积分数为目标函数、以最大 von Mises 应力为约束条件的优化模型。为确保设计结果满足局部应力约束,引入了增强拉格朗日方法。为了提高应力约束拓扑优化的收敛速度,我们开发了一种新的应力约束函数,并将其与之前研究中提出的其他两种应力约束函数进行了比较。基于等几何拓扑优化框架,系统地得出了局部应力约束和体积目标的敏感性分析。通过典型的数值实例,将设计结果与传统的全局应力最小化设计进行了比较。此外,该方法还扩展到了基于等几何分析拓扑优化框架的三维应力约束拓扑优化设计问题,而该问题在等几何分析拓扑优化框架中鲜有研究。本文列举了几个典型的数值实例来证明该方法的有效性。结果表明,所提方法继承了等几何分析的精确几何和元素间高阶连续性的优点,能有效控制结构的最大 von Mises 应力水平,且收敛速度更快。
Isogeometric topology optimization method for design with local stress constraints
Engineering structures are required to meet strength conditions to ensure engineering safety, where the maximum stress level of the structure mainly characterizes the structural strength. This study proposes an isogeometric topology optimization method for the local stress-constrained design. This method establishes an optimization model with volume fraction as the objective function and maximum von Mises stress as the constraint condition. The augmented lagrangian approach is introduced to ensure that the design results satisfy stress constraints locally. To increase the convergence rate of stress-constrained topology optimization, we develop a new stress constraint function, and compare it with the other two stress constraint functions proposed by previous research. Sensitivity analysis of the local stress-constraint and volume objective based on an isogeometric topology optimization framework is systematically derived. The design result is compared with the traditional global stress minimization design through typical numerical examples. In addition, this method is extended to the three-dimensional stress-constrained topology optimization design problem that has rarely been studied in the isogeometric-analysis-based topology optimization framework. Several typical numerical examples are presented to demonstrate the method’s effectiveness. It demonstrates that the proposed method inherits the merits of the exact geometry and high-order continuity between elements of isogeometric analysis and can effectively control the maximum von Mises stress level of structures, with a faster convergence rate.
期刊介绍:
Computers & Structures publishes advances in the development and use of computational methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is wide, and includes papers on establishing appropriate mathematical models and their numerical solution in all areas of mechanics. The journal also includes articles that present a substantial review of a field in the topics of the journal.