Formulation and analysis of variational methods for time integration of linear elastodynamics. (English) Zbl 0862.73078
A general framework for variational formulations of linear elastodynamics is introduced. Variational formulations which originate from the principle of minimum potential energy, the Hellinger-Reissner principle and the Hu-Washizu principle are considered. They are characterized by the weak enforcement of the velocity-displacement relation and of the initial displacement and velocity. Special cases are obtained by a priori enforcement of these conditions. The time integration algorithms obtained by discretizing in the space and time domains are studied with reference to accuracy, stability and high-frequency behaviour.
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74P10 | Optimization of other properties in solid mechanics |
| 74B05 | Classical linear elasticity |
Keywords:
principle of minimum potential energy; Hellinger-Reissner principle; Hu-Washizu principle; stability; high-frequency behaviourReferences:
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