Newmark algorithm for dynamic analysis with Maxwell chain model
Abstract
This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses of viscoelastic structures characterized by a generalized Maxwell model. We depart from a scheme developed for a three-parameter model by Hatada et al. in 2000, which we extend to a generic Maxwell chain and demonstrate that the resulting algorithm can be derived from a suitably discretized Hamilton variational principle. This variational structure manifests itself in an excellent stability and a low artificial damping of the integrator, as we confirm with a mass-spring-dashpot example. After a straightforward generalization to distributed systems, the integrator may find use in, e.g., fracture simulations of laminated glass units, once combined with variationally-based fracture models.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.03255
- arXiv:
- arXiv:1911.03255
- Bibcode:
- 2019arXiv191103255S
- Keywords:
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- Computer Science - Computational Engineering;
- Finance;
- and Science
- E-Print:
- 9 pages, 4 figures, 1 table