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Theoretical modeling and parallel programming of a nonlinear composite finite shell element based on a mixed global-local variational principle

Schürg, Marco (2013)
Theoretical modeling and parallel programming of a nonlinear composite finite shell element based on a mixed global-local variational principle.
Book, Bibliographie

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Abstract

Thin-walled structures made of fiber-reinforced composites possess properties which are in high demand in various engineering fields. In this thesis, a contribution is made to the theoretical and numerical modeling of such materials. The global-local finite shell element presented further develops a nonlinear finite shell element emanating from a mixed variational principle. The underlying shell model is called the global model in this work, since the associated field equations have to be fulfilled for the structure as a whole. The variational principle is extended with a local field equation, which is to be fulfilled at a specific point in the structure. In the context of the finite element formulation this means that the local equation is fulfilled in an integration point. The local field equation is the local equilibrium equation, by which the local displacements and the interlaminar stresses are derived. This part of the model is called the local part. A clearly defined interface between the global and the local part of the model is provided. The path of the interlaminar stresses is computed as part of the variational formulation. The global and local part of the model are not independent of each other. Thus, through the addition of the local model the results of the effective stress resultants are manipulated. In order to circumvent this, an orthogonality condition is introduced, which requires that the addition of the local model to the effective membrane stress resultants and the effective stress couple resultants vanishes. For simulations with the finite element method, the independent fields in the linearized global-local variational principle are approximated with suitable interpolation functions. The global-local finite shell element has five or six global degrees of freedom, three displacements and two or three rotational parameters, since all other fields are eliminated by numeric procedures on the element level. Additionally, an alternative possibility to derive the interlaminar shear stresses is proposed, which can be applied in shell and plate elements and is a post-processing procedure. The capabilities of the global-local finite shell element and the post-processing procedure are illustrated with the help of numerical examples. The addition of the local part of the model leads to a significant increase in computation time, due to the unknowns introduced on the element level. For this reason, the finite element software used in the implementation of the finite shell element is adapted to modern computer architectures with multiple cores and shared memory by parallelizing the implemented code. A number of examples carried out on a modern desktop computer are presented to illustrate the effectiveness of the implemented parallelized code.

Item Type: Book
Erschienen: 2013
Creators: Schürg, Marco
Type of entry: Bibliographie
Title: Theoretical modeling and parallel programming of a nonlinear composite finite shell element based on a mixed global-local variational principle
Language: English
Referees: Gruttmann, Prof. Friedrich ; Wagner, Prof. Werner ; Wackerfuß, Dr.-Ing. Jens
Date: 2013
Place of Publication: Darmstadt
Publisher: Technische Universität Darmstadt, Studienbereich Mechanik
Series: Forschungsberichte des Instituts für Mechanik der Technischen Universität Darmstadt
Series Volume: 27
Refereed: 22 August 2012
Corresponding Links:
Abstract:

Thin-walled structures made of fiber-reinforced composites possess properties which are in high demand in various engineering fields. In this thesis, a contribution is made to the theoretical and numerical modeling of such materials. The global-local finite shell element presented further develops a nonlinear finite shell element emanating from a mixed variational principle. The underlying shell model is called the global model in this work, since the associated field equations have to be fulfilled for the structure as a whole. The variational principle is extended with a local field equation, which is to be fulfilled at a specific point in the structure. In the context of the finite element formulation this means that the local equation is fulfilled in an integration point. The local field equation is the local equilibrium equation, by which the local displacements and the interlaminar stresses are derived. This part of the model is called the local part. A clearly defined interface between the global and the local part of the model is provided. The path of the interlaminar stresses is computed as part of the variational formulation. The global and local part of the model are not independent of each other. Thus, through the addition of the local model the results of the effective stress resultants are manipulated. In order to circumvent this, an orthogonality condition is introduced, which requires that the addition of the local model to the effective membrane stress resultants and the effective stress couple resultants vanishes. For simulations with the finite element method, the independent fields in the linearized global-local variational principle are approximated with suitable interpolation functions. The global-local finite shell element has five or six global degrees of freedom, three displacements and two or three rotational parameters, since all other fields are eliminated by numeric procedures on the element level. Additionally, an alternative possibility to derive the interlaminar shear stresses is proposed, which can be applied in shell and plate elements and is a post-processing procedure. The capabilities of the global-local finite shell element and the post-processing procedure are illustrated with the help of numerical examples. The addition of the local part of the model leads to a significant increase in computation time, due to the unknowns introduced on the element level. For this reason, the finite element software used in the implementation of the finite shell element is adapted to modern computer architectures with multiple cores and shared memory by parallelizing the implemented code. A number of examples carried out on a modern desktop computer are presented to illustrate the effectiveness of the implemented parallelized code.

Alternative Abstract:
Alternative abstract Language

Dünnwandige Strukturen aus Faserverbundwerkstoffen sind in verschiedenen Ingenieurdisziplinen sehr gefragt. Diese Arbeit leistet einen Beitrag zur theoretischen und numerischen Modellierung dieser Materialien. Das vorgestellte global-lokale finite Schalenelement entwickelt ein nichtlineares finites Schalenelement weiter, das aus einem gemischten Variationsprinzip hervorgeht. Das zugrundeliegende Schalenmodell wird in dieser Arbeit das globale Modell genannt, da die zugehörigen Feldgleichungen für die gesamte Struktur erfüllt sein müssen. Das Variationsprinzip wird um eine lokale Feldgleichung erweitert, die in einem bestimmten Punkt der Struktur erfüllt sein muss. Innerhalb der Finite-Elemente-Methode bedeutet dies, dass die lokale Gleichung in einem Integrationspunkt erfüllt wird. Die lokale Feldgleichung ist die Gleichgewichtsbedingung, mit deren Hilfe die interlaminaren Spannungen ermittelt werden. Dieser Teil des Modells wird in dieser Arbeit das lokale Modell genannt. Die Schnittstelle zwischen dem globalen und lokalen Modell ist klar definiert. Der Verlauf der interlaminaren Spannungen wird als Teil der variationellen Formulierung berechnet. Der globale und lokale Teil des Modells sind nicht unabhängig voneinander. Die Einführung des lokalen Modells führt daher zu veränderten Ergebnissen der effektiven Schnittgrößen. Um dies zu umgehen wird eine Orthogonalitätsbedingung eingeführt, die verlangt, dass der Beitrag des lokalen Schalenmodells nicht zu zusätzlichen Normalkräften und Momenten führt. Für Simulationen mit der Finite-Elemente-Methode werden die unabhängigen Felder innerhalb des linearisierten global-lokalen Variationsprinzips mit geeigneten Interpolationsfunktionen approximiert. Das global-lokale finite Schalenelement hat fünf oder sechs Freiheitsgrade, drei Verschiebungen und zwei oder drei Rotationsparameter, da alle weiteren unabhängigen Felder durch numerische Verfahren auf Elementebene eliminiert werden. Zusätzlich wird in dieser Arbeit eine alternative Möglichkeit vorgeschlagen, um die interlaminaren Schubspannungen zu ermitteln, die in Plattenelementen oder Schalenelementen in einem Post-Processing Verfahren angewandt werden kann. Die Wirkungsweisen des global-lokalen Schalenelements und des Post-Processing Verfahrens werden mit Hilfe einiger numerischer Beispiele illustriert. Die Einführung des lokalen Modells führt durch die auf Elementebene eingebrachten zusätzlichen Unbekannten zu einer wesentlichen Erhöhung der Rechenzeit. Aus diesem Grund wird die bei der Implementierung des Schalenelements verwendete Finite-Elemente-Software an moderne Rechnerarchitekturen mit mehreren Prozessoren und einem gemeinsamen Speicher angepasst, indem der implementierte Code parallelisiert wird. Mehrere auf einem modernen Desktop-Computer durchgeführte Beispiele werden dargestellt, um die Effektivität der Parallelisierung zu veranschaulichen.

German
Uncontrolled Keywords: global-local finite shell element, interlaminar stresses, CFRP, laminates, parallel programming
Alternative keywords:
Alternative keywordsLanguage
global-lokales finites Schalenelement, interlaminare Spannungen, CFK, Laminate, parallele ProgrammierungGerman
Classification DDC: 500 Science and mathematics > 500 Science
Divisions: 13 Department of Civil and Environmental Engineering Sciences
13 Department of Civil and Environmental Engineering Sciences > Mechanics
13 Department of Civil and Environmental Engineering Sciences > Mechanics > Solid Body Mechanics
Date Deposited: 02 Jul 2024 22:11
Last Modified: 02 Jul 2024 22:11
PPN:
Referees: Gruttmann, Prof. Friedrich ; Wagner, Prof. Werner ; Wackerfuß, Dr.-Ing. Jens
Refereed / Verteidigung / mdl. Prüfung: 22 August 2012
Alternative keywords:
Alternative keywordsLanguage
global-lokales finites Schalenelement, interlaminare Spannungen, CFK, Laminate, parallele ProgrammierungGerman
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