{"title":"多体动力学的时域有限元法","authors":"Olivier Bauchau","doi":"10.1115/1.4063953","DOIUrl":null,"url":null,"abstract":"Abstract The generalized-αscheme has become the approach of choice for the time integration of the equations of motion of multibody systems. Despite its simplicity, this scheme presents drawbacks: the time step size cannot be changed easily, making it difficult to implement time adaptivity, and the solution of periodic problems cannot be found easily. This paper explores an alternative approach based on the finite element method in time. The basic principles underpinning the approach are presented and both time-continuous and time-discontinuous approaches are investigated. Two types of Galerkin schemes will be presented here: the time-continuous and the time-discontinuous schemes. In the former, the displacement field is continuous across inter-element boundaries, whereas discontinuities or “jumps” are allowed across inter-element boundaries for the latter. Simple problems are treated to identify the best schemes. Families of schemes of various accuracy are presented. The first family, based on time-continuous elements, features schemes that do not present numerical dissipation. Asymptotic annihilation is achieved by the time-discontinuous elements that form the second family. The problem of kinematic constraints is treated within the framework of the finite element method in time. Special emphasis is devoted to the satisfaction of the kinematic constraints and their time derivative within a time element.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"19 5","pages":"0"},"PeriodicalIF":1.9000,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Finite Element Method in Time For Multibody Dynamics\",\"authors\":\"Olivier Bauchau\",\"doi\":\"10.1115/1.4063953\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The generalized-αscheme has become the approach of choice for the time integration of the equations of motion of multibody systems. Despite its simplicity, this scheme presents drawbacks: the time step size cannot be changed easily, making it difficult to implement time adaptivity, and the solution of periodic problems cannot be found easily. This paper explores an alternative approach based on the finite element method in time. The basic principles underpinning the approach are presented and both time-continuous and time-discontinuous approaches are investigated. Two types of Galerkin schemes will be presented here: the time-continuous and the time-discontinuous schemes. In the former, the displacement field is continuous across inter-element boundaries, whereas discontinuities or “jumps” are allowed across inter-element boundaries for the latter. Simple problems are treated to identify the best schemes. Families of schemes of various accuracy are presented. The first family, based on time-continuous elements, features schemes that do not present numerical dissipation. Asymptotic annihilation is achieved by the time-discontinuous elements that form the second family. The problem of kinematic constraints is treated within the framework of the finite element method in time. Special emphasis is devoted to the satisfaction of the kinematic constraints and their time derivative within a time element.\",\"PeriodicalId\":54858,\"journal\":{\"name\":\"Journal of Computational and Nonlinear Dynamics\",\"volume\":\"19 5\",\"pages\":\"0\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-11-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Nonlinear Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4063953\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/1.4063953","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
The Finite Element Method in Time For Multibody Dynamics
Abstract The generalized-αscheme has become the approach of choice for the time integration of the equations of motion of multibody systems. Despite its simplicity, this scheme presents drawbacks: the time step size cannot be changed easily, making it difficult to implement time adaptivity, and the solution of periodic problems cannot be found easily. This paper explores an alternative approach based on the finite element method in time. The basic principles underpinning the approach are presented and both time-continuous and time-discontinuous approaches are investigated. Two types of Galerkin schemes will be presented here: the time-continuous and the time-discontinuous schemes. In the former, the displacement field is continuous across inter-element boundaries, whereas discontinuities or “jumps” are allowed across inter-element boundaries for the latter. Simple problems are treated to identify the best schemes. Families of schemes of various accuracy are presented. The first family, based on time-continuous elements, features schemes that do not present numerical dissipation. Asymptotic annihilation is achieved by the time-discontinuous elements that form the second family. The problem of kinematic constraints is treated within the framework of the finite element method in time. Special emphasis is devoted to the satisfaction of the kinematic constraints and their time derivative within a time element.
期刊介绍:
The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.