Integration of elastic multibody systems by invariant conserving/dissipating algorithms. I: Formulation. II: Numerical schemes and applications

DOI10.1016/S0045-7825(00)00286-3zbMath0990.74024MaRDI QIDQ5938288

Carlo L. Bottasso, Marco Borri, Lorenzo Trainelli

Publication date: 19 August 2002

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

zbMATH Keywords

displacement fieldexponential mapholonomic constraintsdynamic analysisgeometrically nonlinear beamsinvariant conserving/dissipating algorithmsnonlinear flexible multibody systemsparameterization techniquerotation fieldsix-dimensional representation of motion

Mathematics Subject Classification ID

Thin bodies, structures (74K99) Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) Finite difference methods applied to problems in solid mechanics (74S20)

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Uses Software

• RODAS

Cites Work

• Unnamed Item
• On the dynamics in space of rods undergoing large motions - A geometrically exact approach
• The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics
• Energy preserving/decaying schemes for nonlinear beam dynamics using the helicoidal approximation
• Energy decaying scheme for nonlinear beam models
• A new look at finite elements in time: A variational interpretation of Runge-Kutta methods
• On representations and parameterizations of motion
• Robust integration schemes for flexible multibody systems.
• Integrating finite rotations
• On the design of energy preserving and decaying schemes for flexible, nonlinear multi-body systems
• Energy decaying scheme for nonlinear elastic multi-body systems
• An intrinsic beam model based on a helicoidal approximation—Part I: Formulation
• Non‐linear dynamics of three‐dimensional rods: Exact energy and momentum conserving algorithms
• Numerical integration of non‐linear elastic multi‐body systems