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

## 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: 2012
Creators: Schürg, Marco
Title: Theoretical modeling and parallel programming of a nonlinear composite finite shell element based on a mixed global-local variational principle
Language: English
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.

Series Name: Forschungsberichte des Instituts für Mechanik der Technischen Universität Darmstadt
Volume: 27
Publisher: Technische Universität Darmstadt, Studienbereich Mechanik
ISBN: 978-3-935868-27-3
Uncontrolled Keywords: global-local finite shell element, interlaminar stresses, CFRP, laminates, parallel programming
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: 21 Apr 2013 19:55
URN: urn:nbn:de:tuda-tuprints-33070