Structure-Preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics

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.