Contact Force Models for Multibody Dynamics

This book analyzes several compliant contact force models within the context of multibody dynamics, while also revisiting the main issues associated with fundamental contact mechanics. In particular, it presents various contact force models, from linear to nonlinear, from purely elastic to dissipative, and describes their parameters. Addressing the different numerical methods and algorithms for contact problems in multibody systems, the book describes the gross motion of multibody systems by using a two-dimensional formulation based on the absolute coordinates and employs different contact models to represent contact-impact events. Results for selected planar multibody mechanical systems are presented and utilized to discuss the main assumptions and procedures adopted throughout this work. The material provided here indicates that the prediction of the dynamic behavior of mechanical systems involving contact-impact strongly depends on the choice of contact force model. In short, the book provides a comprehensive resource for the multibody dynamics community and beyond on modeling contact forces and the dynamics of mechanical systems undergoing contact-impact events.

1. Introduction, - 1.1 General Issues in Contact Problems.- 1.2 Methods Dealing with Contact-Impact Events.- 1.3 Contact-Impact Problems in Biomechanical Systems.- 1.4 Generality of Contact Force Models for Multibody Dynamics.- References.- 2. Pure Elastic Contact Force Models.- 2.1 Generalized Contact Kinematics.- 2.2 Linear Hooke Contact Model.- 2.3 Nonlinear Hertz Contact Model.- 2.4 Other Elastic Contact Models.- References.- 3. Dissipative Contact Force Models.- 3.1 Linear Kelvin-Voigt Contact Model.- 3.2 Nonlinear Hunt and Crossley Contact Model.- 3.3 Nonlinear Lankarani and Nikravesh Contact Model.- 3.4 Nonlinear Flores et al. Contact Model.- 3.5 Other Dissipative Contact Force Models.- References.- 4. Multibody Systems Formulation.- 4.1 Multibody System Roots and Concept.- 4.2 Coordinate Systems for Multibody Systems Formulation.- 4.3 Kinematic Constraint Equations and Kinematic Analysis.- 4.4 Equations of Motion for Constrained Multibody Systems.- 4.5 Inclusion of Contact Forces in Dynamics Equations.- References.- 5. Numerical Methods in Multibody Systems.- 5.1 Algorithms for Dynamic Analysis of Multibody Systems.- 5.2 Constraints Stabilization Method.- 5.3 Numerical Integration Algorithms.- 5.4 Systems of Linear Equations.- 5.5 Systems of Nonlinear Equations.- References.- 6. Demonstrative Examples of Application.- 6.1 Bouncing Ball.- 6.2 Double Pendulum.- 6.3 Slider-Crank Mechanism.- 6.4 Human Knee Model.- 6.5 Biomechanical Foot Model.- 6.6 Comparative Study of Various Contact Force Models.- References.