A generalized formulation of classical shell models based on tangential differential calculus

Daniel Schöllhammer; Thomas Peter Fries

doi:10.18419/opus-10762

A generalized formulation of classical shell models based on tangential differential calculus

Daniel Schöllhammer, Thomas Peter Fries

Institute of Structural Analysis (2020)

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

Abstract

The Tangential Differential Calculus (TDC) enables the mathematical modeling of general physical phenomena on curved surfaces. Herein, it is applied to reformulate classical models for Kirchhoff-Love and Reissner-Mindlin shells. In contrast to the classical approach, the resulting models do not only apply to parametrized shell geometries but also to implicit ones. All mechanical quantities are defined in the 3D Euclidean coordinate system and no curvilinear coordinates are needed. In addition to classical shell analyses based on the standard FEM, the proposed formulation enables implicit shell analyses based
on recently proposed Cut FEM and Trace FEM, which attract a lot of attention lately

Original language	English
Title of host publication	Berichte der Fachtagung Baustatik - Baupraxis 14
Subtitle of host publication	23. und 24. März 2020, Universität Stuttgart
Editors	M. Bischoff, M. von Scheven, B. Oesterle
Publisher	Universität Stuttgart
Pages	431-438
ISBN (Electronic)	978-3-00-064639-3
DOIs	https://doi.org/10.18419/opus-10762
Publication status	Published - 2020
Event	14. Fachtagung Baustatik - Baupraxis - abgesagt, Germany Duration: 23 Mar 2020 → 24 Mar 2020

Conference

Conference	14. Fachtagung Baustatik - Baupraxis
Country/Territory	Germany
City	abgesagt
Period	23/03/20 → 24/03/20

Fields of Expertise

Information, Communication & Computing

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10.18419/opus-10762Licence: Unspecified

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A generalized formulation of classical shell models based on tangential differential calculus. / Schöllhammer, Daniel; Fries, Thomas Peter.
Berichte der Fachtagung Baustatik - Baupraxis 14: 23. und 24. März 2020, Universität Stuttgart. ed. / M. Bischoff; M. von Scheven; B. Oesterle. Universität Stuttgart, 2020. p. 431-438.

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

Schöllhammer, D & Fries, TP 2020, A generalized formulation of classical shell models based on tangential differential calculus. in M Bischoff, M von Scheven & B Oesterle (eds), Berichte der Fachtagung Baustatik - Baupraxis 14: 23. und 24. März 2020, Universität Stuttgart. Universität Stuttgart, pp. 431-438, 14. Fachtagung Baustatik - Baupraxis, abgesagt, Germany, 23/03/20. https://doi.org/10.18419/opus-10762

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abstract = "The Tangential Differential Calculus (TDC) enables the mathematical modeling of general physical phenomena on curved surfaces. Herein, it is applied to reformulate classical models for Kirchhoff-Love and Reissner-Mindlin shells. In contrast to the classical approach, the resulting models do not only apply to parametrized shell geometries but also to implicit ones. All mechanical quantities are defined in the 3D Euclidean coordinate system and no curvilinear coordinates are needed. In addition to classical shell analyses based on the standard FEM, the proposed formulation enables implicit shell analyses basedon recently proposed Cut FEM and Trace FEM, which attract a lot of attention lately",

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N2 - The Tangential Differential Calculus (TDC) enables the mathematical modeling of general physical phenomena on curved surfaces. Herein, it is applied to reformulate classical models for Kirchhoff-Love and Reissner-Mindlin shells. In contrast to the classical approach, the resulting models do not only apply to parametrized shell geometries but also to implicit ones. All mechanical quantities are defined in the 3D Euclidean coordinate system and no curvilinear coordinates are needed. In addition to classical shell analyses based on the standard FEM, the proposed formulation enables implicit shell analyses basedon recently proposed Cut FEM and Trace FEM, which attract a lot of attention lately

AB - The Tangential Differential Calculus (TDC) enables the mathematical modeling of general physical phenomena on curved surfaces. Herein, it is applied to reformulate classical models for Kirchhoff-Love and Reissner-Mindlin shells. In contrast to the classical approach, the resulting models do not only apply to parametrized shell geometries but also to implicit ones. All mechanical quantities are defined in the 3D Euclidean coordinate system and no curvilinear coordinates are needed. In addition to classical shell analyses based on the standard FEM, the proposed formulation enables implicit shell analyses basedon recently proposed Cut FEM and Trace FEM, which attract a lot of attention lately

U2 - 10.18419/opus-10762

DO - 10.18419/opus-10762

M3 - Conference paper

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BT - Berichte der Fachtagung Baustatik - Baupraxis 14

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Y2 - 23 March 2020 through 24 March 2020

ER -

A generalized formulation of classical shell models based on tangential differential calculus

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