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Basic features of the time finite element approach for dynamics

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Abstract

Very general weak forms may be developed for dynamic systems, the most general being analogous to a Hu-Washizu three-field formulation, thus paralleling well-established weak methods of solid mechanics. In this work two different formulations are developed: a pure displacement formulation and a two-field mixed formulation. With the objective of developing a thorough understanding of the peculiar features of finite elements in time, the relevant methodologies associated with this approach for dynamics are extensively discussed. After having laid the theoretical bases, the finite element approximation and the linearization of the resulting forms are developed, together with a method for the treatment of holonomic and nonholonomic constraints, thus widening the horizons of applicability over the vast world of multibody system dynamics. With the purpose of enlightening on the peculiar numerical behavior of the different approaches, simple but meaningful examples are illustrated. To this aim, significant parallels with elastostatics are emphasized.

Sommario

Due differenti formulazioni agli elementi finiti nel tempo sono presentate in questo lavoro quali casi particolari di una formulazione generale a tre campi: la prima è una formulazione agli spostamenti, mentre la seconda è una formulazione mista dove i campi indipendenti sono costituiti da spostamenti e momenti cinetici. Dopo aver sviluppato la linearizzazione e l'approssimazione agli elementi finiti delle forme, viene discussa una tecnica per il trattamento di vincoli di olonomia ed anolonomia. Le principali caratteristiche numeriche dei due metodi vengono infine evidenziate facendo anche ricorso ad esempli semplici ma significativi.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Marco Borri, Carlo Bottasso & Paolo Mantegazza

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  1. Marco Borri
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  2. Carlo Bottasso
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  3. Paolo Mantegazza
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Borri, M., Bottasso, C. & Mantegazza, P. Basic features of the time finite element approach for dynamics. Meccanica 27, 119–130 (1992). https://doi.org/10.1007/BF00420590

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