Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. (English) Zbl 0764.73096

It is shown that widely used implicit schemes, in particular the classical Newmark family of algorithms and its variants, generally fail to conserve total angular momentum for nonlinear Hamiltonian systems including classical rigid body dynamics, nonlinear elastodynamics, nonlinear rods and nonlinear shells. A general class of implicit time- stepping algorithms is presented which preserves exactly the conservation laws present in a general Hamiltonian system with symmetry, in particular the total angular momentum and the total energy. A complete analysis of these algorithms and a related class of schemes referred to as symplectic integrators is given.


74S20 Finite difference methods applied to problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
70-08 Computational methods for problems pertaining to mechanics of particles and systems
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