An energy and momentum conserving method for rigid–flexible body dynamics

In this work, an energy and momentum conserving method is developed for doing coupled flexible and rigid body dynamics. The main focus is on the bilateral connection of flexible finite elements to rigid bodies. The coupling of rigid bodies at joints is also introduced. Existing conserving algorithms for individual (un-coupled) rigid and flexible bodies are exploited and modified for the coupled system. By using the appropriate rigid body rotational update and generalized force definitions, the resulting rigid-flexible and rigid-rigid systems are unconditionally stable and conserve linear and angular momentum. The conservation and stability properties are demonstrated in numerical simulation.

[1]  J. C. Simo,et al.  A new energy and momentum conserving algorithm for the non‐linear dynamics of shells , 1994 .

[2]  Thomas J. R. Hughes,et al.  FINITE-ELEMENT METHODS FOR NONLINEAR ELASTODYNAMICS WHICH CONSERVE ENERGY. , 1978 .

[3]  J. C. Simo,et al.  A three-dimensional finite-strain rod model. Part II: Computational aspects , 1986 .

[4]  T. Hughes,et al.  Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis , 1980 .

[5]  J. C. Simo,et al.  Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum , 1991 .

[6]  R. A. Spurrier.  Comment on " Singularity-Free Extraction of a Quaternion from a Direction-Cosine Matrix" , 1978 .

[7]  B. N. Maker,et al.  Rigid bodies for metal forming analysis with NIKE3D , 1995 .

[8]  T. Hughes.  Generalization of selective integration procedures to anisotropic and nonlinear media , 1980 .

[9]  J. C. Simo,et al.  On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach , 1988 .

[10]  J. C. Simo,et al.  The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics , 1992 .

[11]  J. C. Simo,et al.  Non-linear dynamics of three-dimensional rods: Exact energy and momentum conserving algorithms , 1995 .

[12]  Oscar Gonzalez,et al.  Exact energy and momentum conserving algorithms for general models in nonlinear elasticity , 2000 .

[13]  John M. Hansen,et al.  Unconditionally energy stable implicit time integration: application to multibody system analysis and design , 2000 .

[14]  J. M. Goicolea,et al.  Dynamic analysis of rigid and deformable multibody systems with penalty methods and energy-momentum schemes , 2000 .