Comparison of Moreau-type integrators based on the time finite element discretization of the virtual action

Giuseppe Capobianco; Tom Winandy; Simon R. Eugster; Remco I. Leine

Comparison of Moreau-type integrators based on the time finite element discretization of the virtual action

Giuseppe Capobianco
, Tom Winandy
, Simon R. Eugster
, Remco I. Leine

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

In this paper, we derive and compare three integrators for nonsmooth finite dimensional mechanical systems by discretizing the principle of virtual action with finite elements in time. As shape functions, linear Lagrangian polynomials are used. The different integrators are derived by applying different quadrature rules for the discretization of the strong or the weak variational form of the
virtual action. After the discretization, the constitutive laws for the contact forces are introduced, resulting in Moreau’s time-stepping scheme and two other schemes. Several examples are used to compare these integrators in terms of longterm performance.

Original language	English
Title of host publication	Proceedings of the 9th European Nonlinear Dynamics Conference
Editors	Gábor Stépán, Gábor Csernák
Publication status	Published - 2017
Externally published	Yes

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title = "Comparison of Moreau-type integrators based on the time finite element discretization of the virtual action",

abstract = "In this paper, we derive and compare three integrators for nonsmooth finite dimensional mechanical systems by discretizing the principle of virtual action with finite elements in time. As shape functions, linear Lagrangian polynomials are used. The different integrators are derived by applying different quadrature rules for the discretization of the strong or the weak variational form of the virtual action. After the discretization, the constitutive laws for the contact forces are introduced, resulting in Moreau{\textquoteright}s time-stepping scheme and two other schemes. Several examples are used to compare these integrators in terms of longterm performance. ",

author = "Giuseppe Capobianco and Tom Winandy and Eugster, \{Simon R.\} and Leine, \{Remco I.\}",

year = "2017",

language = "English",

editor = "G{\'a}bor St{\'e}p{\'a}n and G{\'a}bor Csern{\'a}k",

booktitle = "Proceedings of the 9th European Nonlinear Dynamics Conference",

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Comparison of Moreau-type integrators based on the time finite element discretization of the virtual action. / Capobianco, Giuseppe; Winandy, Tom; Eugster, Simon R. et al.
Proceedings of the 9th European Nonlinear Dynamics Conference. ed. / Gábor Stépán; Gábor Csernák. 2017.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Comparison of Moreau-type integrators based on the time finite element discretization of the virtual action

AU - Capobianco, Giuseppe

AU - Winandy, Tom

AU - Eugster, Simon R.

AU - Leine, Remco I.

PY - 2017

Y1 - 2017

N2 - In this paper, we derive and compare three integrators for nonsmooth finite dimensional mechanical systems by discretizing the principle of virtual action with finite elements in time. As shape functions, linear Lagrangian polynomials are used. The different integrators are derived by applying different quadrature rules for the discretization of the strong or the weak variational form of the virtual action. After the discretization, the constitutive laws for the contact forces are introduced, resulting in Moreau’s time-stepping scheme and two other schemes. Several examples are used to compare these integrators in terms of longterm performance.

AB - In this paper, we derive and compare three integrators for nonsmooth finite dimensional mechanical systems by discretizing the principle of virtual action with finite elements in time. As shape functions, linear Lagrangian polynomials are used. The different integrators are derived by applying different quadrature rules for the discretization of the strong or the weak variational form of the virtual action. After the discretization, the constitutive laws for the contact forces are introduced, resulting in Moreau’s time-stepping scheme and two other schemes. Several examples are used to compare these integrators in terms of longterm performance.

M3 - Conference contribution

BT - Proceedings of the 9th European Nonlinear Dynamics Conference

A2 - Stépán, Gábor

A2 - Csernák, Gábor

ER -

Comparison of Moreau-type integrators based on the time finite element discretization of the virtual action

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