On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. I: Low-order methods for two model problems and nonlinear elastodynamics. (English) Zbl 1008.74035

For time-stepping algorithms that exhibit numerical dissipation in high-frequency range, the authors present a formulation in the general context of nonlinear dynamics. They examine existing and new methods for nonlinear elastic spring/mass systems and consider a simplified model of thin elastic beams and the fully nonlinear problem of elastodynamics. The new dissipative schemes consist of a modified stress formula together with a modified dynamic equation relating displacements and velocities. Representative numerical simulations in nonlinear three-dimensional elastodynamics are performed by using the finite element method.


74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics


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