Galerkin-based multi-scale time integration for nonlinear structural dynamics

Matthias Bartelt, Michael Gross
Chair of Applied Mechanics and Dynamics, Chemnitz University of Technology, D-09107 Chemnitz, Germany
Applied Mathematics and Mechanics, 2014


   title={Galerkin-based multi-scale time integration for nonlinear structural dynamics},

   author={Bartelt, Matthias and Gro{ss}, Michael},

   journal={Proceedings in Applied Mathematics and Mechanics},





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This paper deals with a Galerkin-based multi-scale time integration of a viscoelastic rope model. Using Hamilton’s dynamical formulation, Newton’s equation of motion as a second-order partial differential equation is transformed into two coupled first order partial differential equations in time. The considered finite viscoelastic deformations are described by means of a deformation-like internal variable determined by a first order ordinary differential equation in time. The corresponding multi-scale time-integration is based on a Petrov-Galerkin approximation of all time evolution equations, leading to a new family of time stepping schemes with different accuracy orders in the state variables. The resulting nonlinear algebraic time evolution equations are solved by a multi-level Newton-Raphson method. Realizing this transient numerical simulation, we also demonstrates a parallelized solution of the viscous evolution equation in CUDA.
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