NEWMARK ALGORITHM FOR DYNAMIC ANALYSIS WITH MAXWELL CHAIN MODEL

Jaroslav Schmidt; Tomáš Janda; Alena Zemanová; Jan Zeman; Michal Šejnoha

doi:10.14311/AP.2020.60.0502

Authors

Jaroslav Schmidt Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Praha, Czech Republic https://orcid.org/0000-0002-1174-2822
Tomáš Janda Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Praha, Czech Republic
Alena Zemanová Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Praha, Czech Republic https://orcid.org/0000-0002-7613-2099
Jan Zeman Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Praha, Czech Republic https://orcid.org/0000-0003-2503-8120
Michal Šejnoha Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Praha, Czech Republic

DOI:

https://doi.org/10.14311/AP.2020.60.0502

Keywords:

Newmark method, Maxwell chain model, Variational integrators

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. [1], 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.

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