{"title":"使用路径跟踪法寻找用还原传递矩阵法建模的多体系统的静态平衡点","authors":"Xizhe Zhang, Xiaoting Rui, Jianshu Zhang, Lina Zhang, Junjie Gu","doi":"10.1007/s11044-024-09996-y","DOIUrl":null,"url":null,"abstract":"<p>Finding the stable static equilibrium position of multibody systems is a well-known problem. Dynamic relaxation methods are frequently utilized in engineering, however, they often require a significant amount of time. Alternatively, most commercial software employs the Newton–Raphson iterative method to solve a set of nonlinear equations to find the equilibrium position directly, in which the time derivatives of any quantity are set to zero. Nevertheless, this approach is highly dependent on initial conditions and can only find one equilibrium position for a specific initial condition, no matter how many degrees of freedom a system has. A path-following method is implemented in this paper to find the equilibrium position of the multibody system by using the reduced multibody system transfer matrix method to evaluate the acceleration functions and its Jacobian matrix, where the notion of direct differentiation is applied. The solution curves for changing generalized accelerations are then tracked using the arc-length method to obtain candidate equilibrium states if they vanish and identify the stable static equilibrium position. To demonstrate the effectiveness of the proposed method, numerical examples are presented, which provide a detailed overview of the complete computational flow.</p>","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Use of a path-following method for finding static equilibria of multibody systems modeled by the reduced transfer matrix method\",\"authors\":\"Xizhe Zhang, Xiaoting Rui, Jianshu Zhang, Lina Zhang, Junjie Gu\",\"doi\":\"10.1007/s11044-024-09996-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Finding the stable static equilibrium position of multibody systems is a well-known problem. Dynamic relaxation methods are frequently utilized in engineering, however, they often require a significant amount of time. Alternatively, most commercial software employs the Newton–Raphson iterative method to solve a set of nonlinear equations to find the equilibrium position directly, in which the time derivatives of any quantity are set to zero. Nevertheless, this approach is highly dependent on initial conditions and can only find one equilibrium position for a specific initial condition, no matter how many degrees of freedom a system has. A path-following method is implemented in this paper to find the equilibrium position of the multibody system by using the reduced multibody system transfer matrix method to evaluate the acceleration functions and its Jacobian matrix, where the notion of direct differentiation is applied. The solution curves for changing generalized accelerations are then tracked using the arc-length method to obtain candidate equilibrium states if they vanish and identify the stable static equilibrium position. To demonstrate the effectiveness of the proposed method, numerical examples are presented, which provide a detailed overview of the complete computational flow.</p>\",\"PeriodicalId\":49792,\"journal\":{\"name\":\"Multibody System Dynamics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-06-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Multibody System Dynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s11044-024-09996-y\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Multibody System Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s11044-024-09996-y","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Use of a path-following method for finding static equilibria of multibody systems modeled by the reduced transfer matrix method
Finding the stable static equilibrium position of multibody systems is a well-known problem. Dynamic relaxation methods are frequently utilized in engineering, however, they often require a significant amount of time. Alternatively, most commercial software employs the Newton–Raphson iterative method to solve a set of nonlinear equations to find the equilibrium position directly, in which the time derivatives of any quantity are set to zero. Nevertheless, this approach is highly dependent on initial conditions and can only find one equilibrium position for a specific initial condition, no matter how many degrees of freedom a system has. A path-following method is implemented in this paper to find the equilibrium position of the multibody system by using the reduced multibody system transfer matrix method to evaluate the acceleration functions and its Jacobian matrix, where the notion of direct differentiation is applied. The solution curves for changing generalized accelerations are then tracked using the arc-length method to obtain candidate equilibrium states if they vanish and identify the stable static equilibrium position. To demonstrate the effectiveness of the proposed method, numerical examples are presented, which provide a detailed overview of the complete computational flow.
期刊介绍:
The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations.
The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.