Presents a state-of-the-art review of structure-preservingnumerical methods for constrained mechanical systems
Offers contemporary treatment of numerical methods forflexible multibody dynamics
Outlines a comprehensive approach that yields an integratedsimulation tool for flexible mechanism analysis
This book focuses on structure-preserving numerical methodsfor flexible multibody dynamics, including nonlinear elastodynamics andgeometrically exact models for beams and shells. It also deals with the newlyemerging class of variational integrators as well as Lie-group integrators. Itdiscusses two alternative approaches to the discretization in space ofnonlinear beams and shells. Firstly, geometrically exact formulations, whichare typically used in the finite element community and, secondly, the absolutenodal coordinate formulation, which is popular in the multibody dynamicscommunity. Concerning the discretization in time, the energy-momentum methodand its energy-decaying variants are discussed. It also addresses a number ofissues that have arisen in the wake of the structure-preserving discretizationin space. Among them are the parameterization of finite rotations, theincorporation of algebraic constraints and the computer implementation of thevarious numerical methods. The practical application of structure-preservingmethods is illustrated by a number of examples dealing with, among others,nonlinear beams and shells, large deformation problems, long-term simulationsand coupled thermo-mechanical multibody systems. In addition it links novel timeintegration methods to frequently used methods in industrial multibody systemsimulation.
The Energy-momentum method for flexible multibody dynamics: EM integrators for elastic cosserat points.- EM integrators for rigid body dynamics.- EM integrators for flexible multibody dynamics.- Foundations of time integration methods: basics of time integration in nonlinear system dynamics.- Time integration in industrial multibody system simulation.- Time integration methods for differential equations on manifolds.- Generalized-alpha Lie group time integration.- Spurious oscillations in generalized-alpha time integration.- The Absolute Nodal Coordinate Formulation: Introduction to ANCF.- 2D Bernoulli-Euler (thin) ANC element.- 3D shear and cross section deformable ANC element.- 2D shear and cross section deformable fully parameterized ANCF.- 2D shear and cross section deformable gradient deficient ANCF.- Selection of boundary conditions for 2D ANC elements.- 3D shear and cross section deformable ANC elements.- Variants of the energy-momentum method: Numerical time integration in solid mechanics: the role of dissipation.- The discrete gradient.- High frequency dissipative methods for nonlinear solid dynamics.- Energy decaying, momentum conserving methods.- The Energy-Entropy-Momentum method.- Conservative and dissipative methods in flexible multibody dynamics: Second order time integrators.- Conservative / dissipative time integration schemes.- Lie group formalisms.- A brief course on variational integrators
This book focuses on structure-preserving numerical methodsfor flexible multibody dynamics, including nonlinear elastodynamics andgeometrically exact models for beams and shells. It also deals with the newlyemerging class of variational integrators as well as Lie-group integrators. Itdiscusses two alternative approaches to the discretization in space ofnonlinear beams and shells. Firstly, geometrically exact formulations, whichare typically used in the finite element community and, secondly, the absolutenodal coordinate formulation, which is popular in the multibody dynamicscommunity. Concerning the discretization in time, the energy-momentum methodand its energy-decaying variants are discussed. It also addresses a number ofissues that have arisen in the wake of the structure-preserving discretizationin space. Among them are the parameterization of finite rotations, theincorporation of algebraic constraints and the computer implementation of thevarious numerical methods. The practical application of structure-preservingmethods is illustrated by a number of examples dealing with, among others,nonlinear beams and shells, large deformation problems, long-term simulationsand coupled thermo-mechanical multibody systems. In addition it links novel timeintegration methods to frequently used methods in industrial multibody systemsimulation.
High Frequency Dissipative Integration Schemes for Linear andNonlinear Elastodynamics.- Energy-Momentum Integrators for Elastic CosseratPoints, Rigid Bodies, and Multibody Systems.- A Lie Algebra Approach to LieGroup Time Integration of Constrained Systems.- The Absolute Nodal CoordinateFormulation.- A Brief Introduction to Variational Integrators.
Inhaltsverzeichnis
The Energy-momentum method for flexible multibody dynamics: EM integrators for elastic cosserat points.- EM integrators for rigid body dynamics.- EM integrators for flexible multibody dynamics.- Foundations of time integration methods: basics of time integration in nonlinear system dynamics.- Time integration in industrial multibody system simulation.- Time integration methods for differential equations on manifolds.- Generalized-alpha Lie group time integration.- Spurious oscillations in generalized-alpha time integration.- The Absolute Nodal Coordinate Formulation: Introduction to ANCF.- 2D Bernoulli-Euler (thin) ANC element.- 3D shear and cross section deformable ANC element.- 2D shear and cross section deformable fully parameterized ANCF.- 2D shear and cross section deformable gradient deficient ANCF.- Selection of boundary conditions for 2D ANC elements.- 3D shear and cross section deformable ANC elements.- Variants of the energy-momentum method: Numerical time integration in solid mechanics: the role of dissipation.- The discrete gradient.- High frequency dissipative methods for nonlinear solid dynamics.- Energy decaying, momentum conserving methods.- The Energy-Entropy-Momentum method.- Conservative and dissipative methods in flexible multibody dynamics: Second order time integrators.- Conservative / dissipative time integration schemes.- Lie group formalisms.- A brief course on variational integrators
Klappentext
This book focuses on structure-preserving numerical methods
for flexible multibody dynamics, including nonlinear elastodynamics and
geometrically exact models for beams and shells. It also deals with the newly
emerging class of variational integrators as well as Lie-group integrators. It
discusses two alternative approaches to the discretization in space of
nonlinear beams and shells. Firstly, geometrically exact formulations, which
are typically used in the finite element community and, secondly, the absolute
nodal coordinate formulation, which is popular in the multibody dynamics
community. Concerning the discretization in time, the energy-momentum method
and its energy-decaying variants are discussed. It also addresses a number of
issues that have arisen in the wake of the structure-preserving discretization
in space. Among them are the parameterization of finite rotations, the
incorporation of algebraic constraints and the computer implementation of the
various numerical methods. The practical application of structure-preserving
methods is illustrated by a number of examples dealing with, among others,
nonlinear beams and shells, large deformation problems, long-term simulations
and coupled thermo-mechanical multibody systems. In addition it links novel time
integration methods to frequently used methods in industrial multibody system
simulation.
Presents a state-of-the-art review of structure-preserving
numerical methods for constrained mechanical systems
Offers contemporary treatment of numerical methods for
flexible multibody dynamics
Outlines a comprehensive approach that yields an integrated
simulation tool for flexible mechanism analysis
Includes supplementary material: sn.pub/extras
