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Finite Element Methods for Thin Structures with Applications in Solid MechanicsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2013 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Umeå universitet , 2013. , p. vi, 18
##### Series

Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 54
##### Keyword [en]

a priori error estimation, finite element method, discontinuous Galerkin, corotation, Kirchhoff-Love plate, curved beam, biharmonic equation
##### National Category

Computational Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-79297ISBN: 978-91-7459-653-3 (print)ISBN: 978-91-7459-654-0 (print)OAI: oai:DiVA.org:umu-79297DiVA, id: diva2:640426
##### Public defence

2013-09-06, S205h, Samhällsvetarhuset, Umeå universitet, Umeå, 10:15 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt603",{id:"formSmash:j_idt603",widgetVar:"widget_formSmash_j_idt603",multiple:true});
##### Supervisors

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#####

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Available from: 2013-08-16 Created: 2013-08-13 Last updated: 2013-08-16Bibliographically approved
##### List of papers

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers.

In the first paper we introduce a thread model for use in interactive simulation. Based on a three-dimensional beam model, a corotational approach is used for interactive simulation speeds in combination with adaptive mesh resolution to maintain accuracy.

In the second paper we present a family of continuous piecewise linear finite elements for thin plate problems. Patchwise reconstruction of a discontinuous piecewise quadratic deflection field allows us touse a discontinuous Galerkin method for the plate problem. Assuming a criterion on the reconstructions is fulfilled we prove a priori error estimates in energy norm and *L*^{2}-norm and provide numerical results to support our findings.

The third paper deals with the biharmonic equation on a surface embedded in *R*^{3}. We extend theory and formalism, developed for the approximation of solutions to the Laplace-Beltrami problem on an implicitly defined surface, to also cover the biharmonic problem. A priori error estimates for a continuous/discontinuous Galerkin method is proven in energy norm and *L*^{2}-norm, and we support the theoretical results by numerical convergence studies for problems on a sphere and on a torus.

In the fourth paper we consider finite element modeling of curved beams in *R*^{3}. We let the geometry of the beam be implicitly defined by a vector distance function. Starting from the three-dimensional equations of linear elasticity, we derive a weak formulation for a linear curved beam expressed in global coordinates. Numerical results from a finite element implementation based on these equations are compared with classical results.

1. Interactive simulation of a continuum mechanics based torsional thread$(function(){PrimeFaces.cw("OverlayPanel","overlay372833",{id:"formSmash:j_idt656:0:j_idt663",widgetVar:"overlay372833",target:"formSmash:j_idt656:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Continuous piecewise linear finite elements for the Kirchhoff–Love plate equation$(function(){PrimeFaces.cw("OverlayPanel","overlay473342",{id:"formSmash:j_idt656:1:j_idt663",widgetVar:"overlay473342",target:"formSmash:j_idt656:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. A continuous/discontinuous Galerkin method and a priori error estimates for the biharmonic problem on surfaces$(function(){PrimeFaces.cw("OverlayPanel","overlay640280",{id:"formSmash:j_idt656:2:j_idt663",widgetVar:"overlay640280",target:"formSmash:j_idt656:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Intrinsic finite element modeling of curved beams$(function(){PrimeFaces.cw("OverlayPanel","overlay640293",{id:"formSmash:j_idt656:3:j_idt663",widgetVar:"overlay640293",target:"formSmash:j_idt656:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
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