Computational flexible multibody dynamics. A differential-algebraic approach.

*(English)*Zbl 1279.70002
Differential-Algebraic Equations Forum. Berlin: Springer (ISBN 978-3-642-35157-0/pbk; 978-3-642-35158-7/ebook). xii, 249 p. (2013).

Flexible multibody dynamics is a research field with various applications in vehicle analysis, aerospace engineering, robotics, and biomechanics. The present monograph provides comprehensive information on both the mathematical framework as well as the numerical methods for flexible multibody dynamics. The interplay of modeling and numerics is a key feature in multibody flexible dynamics, and mainly determines the methodology chosen in the monograph. This is reflected by the organization into two main parts with four chapters each.

The first part “Mathematical models” considers the general mechanical theory of multibody systems, reference frames, constraint equations, rigid multibody dynamics, elastic motion and flexible multibody dynamics. Special attention is paid to the analysis of equations of constrained mechanical motion and to the theory of differential-algebraic equations.

The second part “Numerical methods” considers how the spatial discretization of a flexible multibody system leads to differential-algebraic equations in time. Further, a chapter is devoted to stiff mechanical systems and another one to time-integration methods. At the end of the monograph, some of the numerical issues discussed in the book are illustrated with case studies.

The intended audience for this book consists not only of graduate students, Ph.D. students and scientists working in the field of flexible multibody dynamics, but also of those interested in time-dependent partial differential equations and heterogeneous problems with multiple time scales.

The first part “Mathematical models” considers the general mechanical theory of multibody systems, reference frames, constraint equations, rigid multibody dynamics, elastic motion and flexible multibody dynamics. Special attention is paid to the analysis of equations of constrained mechanical motion and to the theory of differential-algebraic equations.

The second part “Numerical methods” considers how the spatial discretization of a flexible multibody system leads to differential-algebraic equations in time. Further, a chapter is devoted to stiff mechanical systems and another one to time-integration methods. At the end of the monograph, some of the numerical issues discussed in the book are illustrated with case studies.

The intended audience for this book consists not only of graduate students, Ph.D. students and scientists working in the field of flexible multibody dynamics, but also of those interested in time-dependent partial differential equations and heterogeneous problems with multiple time scales.

Reviewer: Clementina Mladenova (Sofia)

##### MSC:

70-02 | Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems |

70E55 | Dynamics of multibody systems |

70-08 | Computational methods for problems pertaining to mechanics of particles and systems |

74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |