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On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. II: Second-order methods. (English) Zbl 1068.74022

[For part I see the authors, ibid. 190, No. 20–21, 2603–2649 (2001; Zbl 1008.74035).]
From the summary: We present the formulation of a new high-frequency dissipative time-stepping algorithm for nonlinear elastodynamics that is second-order accurate in time. The new scheme exhibits unconditional energy dissipation and momentum conservation (and thus the given name of energy-dissipative, momentum-conserving second-order scheme), leading also to the conservation of the relative equilibria of the underlying physical system. The unconditional character of these properties applies not only with respect to the time step size but, equally important, with respect to the considered elastic potential. Moreover, the dissipation properties are fully controlled through an algorithmic parameter, reducing to existing fully conserving schemes, is desired. The design of the new algorithm if described in detail, including a complete analysis of its dissipation/conservation properties in the fully nonlinear range of finite elasticity.

MSC:

74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity

Citations:

Zbl 1008.74035

Software:

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References:

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