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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.

MSC:

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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