{"title":"有约束条件的 Cosserat-rod 模型半显式时间积分的李群局部坐标","authors":"Denise Tumiotto, Martin Arnold","doi":"10.1007/s11044-024-10002-8","DOIUrl":null,"url":null,"abstract":"<p>Explicit Runge–Kutta methods are the gold standard of time-integration methods for nonstiff problems in system dynamics since they combine a small numerical effort per time step with high accuracy, error control, and straightforward implementation. For the analysis of beam dynamics, we couple them with a local coordinates approach in a Lie group setting to address large rotations. Stiff shear forces and inextensibility conditions are enforced by internal constraints in a coarse-grid discretization of a geometrically exact beam model. The resulting nonstiff constrained systems are handled by a half-explicit approach that relies on the constraints at velocity level and avoids all kinds of Newton–Raphson iteration. We construct half-explicit Runge–Kutta Lie group methods of order up to five that are equipped with an adaptive step-size strategy using embedded Runge–Kutta pairs for error estimation. The methods are tested successfully for a roll-up maneuver of a flexible beam and for the classical flying-spaghetti benchmark.</p>","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local coordinates on Lie groups for half-explicit time integration of Cosserat-rod models with constraints\",\"authors\":\"Denise Tumiotto, Martin Arnold\",\"doi\":\"10.1007/s11044-024-10002-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Explicit Runge–Kutta methods are the gold standard of time-integration methods for nonstiff problems in system dynamics since they combine a small numerical effort per time step with high accuracy, error control, and straightforward implementation. For the analysis of beam dynamics, we couple them with a local coordinates approach in a Lie group setting to address large rotations. Stiff shear forces and inextensibility conditions are enforced by internal constraints in a coarse-grid discretization of a geometrically exact beam model. The resulting nonstiff constrained systems are handled by a half-explicit approach that relies on the constraints at velocity level and avoids all kinds of Newton–Raphson iteration. We construct half-explicit Runge–Kutta Lie group methods of order up to five that are equipped with an adaptive step-size strategy using embedded Runge–Kutta pairs for error estimation. The methods are tested successfully for a roll-up maneuver of a flexible beam and for the classical flying-spaghetti benchmark.</p>\",\"PeriodicalId\":49792,\"journal\":{\"name\":\"Multibody System Dynamics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-06-20\",\"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/s11044-024-10002-8\",\"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/s11044-024-10002-8","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Local coordinates on Lie groups for half-explicit time integration of Cosserat-rod models with constraints
Explicit Runge–Kutta methods are the gold standard of time-integration methods for nonstiff problems in system dynamics since they combine a small numerical effort per time step with high accuracy, error control, and straightforward implementation. For the analysis of beam dynamics, we couple them with a local coordinates approach in a Lie group setting to address large rotations. Stiff shear forces and inextensibility conditions are enforced by internal constraints in a coarse-grid discretization of a geometrically exact beam model. The resulting nonstiff constrained systems are handled by a half-explicit approach that relies on the constraints at velocity level and avoids all kinds of Newton–Raphson iteration. We construct half-explicit Runge–Kutta Lie group methods of order up to five that are equipped with an adaptive step-size strategy using embedded Runge–Kutta pairs for error estimation. The methods are tested successfully for a roll-up maneuver of a flexible beam and for the classical flying-spaghetti benchmark.
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.