{"title":"Form-finding for tensegrity structures based on the equilibrium equation","authors":"Ziying Cao, Ani Luo, Yaming Feng, Heping Liu","doi":"10.1016/j.mechrescom.2024.104256","DOIUrl":null,"url":null,"abstract":"<div><p>Finding form is a critical step in designing tensegrity structures. On the condition that the partial node coordinates, topology, and a bar/cable attribute (the force density of bar is -1 and the force density of cable is 1.) are known, a form-finding method, which is used to find the remaining node coordinates and the force density relation between elements, is proposed in this paper. Firstly, the equilibrium conditions of the tensegrity system are analyzed, and the equilibrium equation is established. Secondly, the variables that must be solved are set and substituted into the equilibrium equation, and the target equation with the variables is built. The Levenberg-Marquardt method with a damping parameter updating strategy is introduced to solve the least squares problem by transforming the equilibrium equation problem into the least squares problem. The form-finding process is performed by solving the least squares formula. Three examples demonstrate the efficiency and accuracy of searching for self-equilibrium configurations.</p></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics Research Communications","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0093641324000144","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Finding form is a critical step in designing tensegrity structures. On the condition that the partial node coordinates, topology, and a bar/cable attribute (the force density of bar is -1 and the force density of cable is 1.) are known, a form-finding method, which is used to find the remaining node coordinates and the force density relation between elements, is proposed in this paper. Firstly, the equilibrium conditions of the tensegrity system are analyzed, and the equilibrium equation is established. Secondly, the variables that must be solved are set and substituted into the equilibrium equation, and the target equation with the variables is built. The Levenberg-Marquardt method with a damping parameter updating strategy is introduced to solve the least squares problem by transforming the equilibrium equation problem into the least squares problem. The form-finding process is performed by solving the least squares formula. Three examples demonstrate the efficiency and accuracy of searching for self-equilibrium configurations.
期刊介绍：
Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide:
• a fast means of communication
• an exchange of ideas among workers in mechanics
• an effective method of bringing new results quickly to the public
• an informal vehicle for the discussion
• of ideas that may still be in the formative stages
The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.
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