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.