NEWMARK ALGORITHM FOR DYNAMIC ANALYSIS WITH MAXWELL CHAIN MODEL
Keywords:Newmark method, Maxwell chain model, Variational integrators
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. , 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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Copyright (c) 2020 Jaroslav Schmidt, Tomáš Janda, Alena Zemanová, Jan Zeman, Michal Šejnoha
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