Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Cut finite element modeling of linear membranes
Högskolan i Jönköping, Tekniska Högskolan, JTH. Forskningsmiljö Produktutveckling - Simulering och optimering.
Högskolan i Jönköping, Tekniska Högskolan, JTH, Produktutveckling. Högskolan i Jönköping, Tekniska Högskolan, JTH. Forskningsmiljö Produktutveckling - Simulering och optimering.ORCID-id: 0000-0001-7352-1550
Umeå University.
2016 (engelsk)Inngår i: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 310, s. 98-111Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus, i.e., with the equilibrium equations pointwise projected onto the tangent plane of the surface to create a pointwise planar problem in the tangential direction. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization of the membrane comes from a Galerkin method using the restriction of 3D basis functions (linear or trilinear) to the surface representing the membrane. In the case of coupling to 3D elasticity, we view the membrane as giving additional stiffness contributions to the standard stiffness matrix resulting from the discretization of the three-dimensional continuum.

sted, utgiver, år, opplag, sider
2016. Vol. 310, s. 98-111
Emneord [en]
Cut finite element method, Embedded membrane, Membrane shell, Tangential derivative
HSV kategori
Identifikatorer
URN: urn:nbn:se:hj:diva-28420DOI: 10.1016/j.cma.2016.05.018ISI: 000384859400005Scopus ID: 2-s2.0-84979299087OAI: oai:DiVA.org:hj-28420DiVA, id: diva2:875536
Tilgjengelig fra: 2015-12-01 Laget: 2015-12-01 Sist oppdatert: 2018-01-10bibliografisk kontrollert
Inngår i avhandling
1. Finite element methods on surfaces
Åpne denne publikasjonen i ny fane eller vindu >>Finite element methods on surfaces
2015 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
Abstract [en]

The purpose of this thesis is to improve numerical simulations of surface problems. Two novel computational concepts are analyzed and applied on two surface problems; minimal surface problems and elastic membrane problems. The concept of tangential projection implies that direct computation on the surface is made possible compared to the classical approach of mapping 2D parametric surfaces to 3D surfaces by means of differential geometry operators. The second concept presented is the cut finite element method, in which the basic idea of discretization is to embed the d- 1-dimensional surface in a d-dimensional mesh and use the basis functions of a higher dimensional mesh but integrate over the surface. The aim of this thesis is to present the basics of the two main approaches and to provide details on the implementation.

sted, utgiver, år, opplag, sider
Jönköping: Jönköping University, School of Engineering, 2015. s. 41
Serie
JTH Dissertation Series ; 12
HSV kategori
Identifikatorer
urn:nbn:se:hj:diva-28424 (URN)978-91-87289-13-2 (ISBN)
Veileder
Forskningsfinansiär
Swedish Research Council, 2011-4992
Tilgjengelig fra: 2015-12-01 Laget: 2015-12-01 Sist oppdatert: 2018-01-10bibliografisk kontrollert
2. Finite element methods for surface problems
Åpne denne publikasjonen i ny fane eller vindu >>Finite element methods for surface problems
2017 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

The purpose of this thesis is to further develop numerical methods for solving surface problems by utilizing tangential calculus and the trace finite element method. Direct computation on the surface is possible by the use of tangential calculus, in contrast to the classical approach of mapping 2D parametric surfaces to 3D surfaces by means of differential geometry operators. Using tangential calculus, the problem formulation is only dependent on the position and normal vectors of the 3D surface. Tangential calculus thus enables a clean, simple and inexpensive formulation and implementation of finite element methods for surface problems. Meshing techniques are greatly simplified from the end-user perspective by utilizing an unfitted finite element method called the Trace Finite Element Method, in which the basic idea is to embed the surface in a higher dimensional mesh and use the shape functions of this background mesh for the discretization of the partial differential equation. This method makes it possible to model surfaces implicitly and solve surface problems without the need for expensive meshing/re-meshing techniques especially for moving surfaces or surfaces embedded in 3D solids, so called embedded interface problems. Using these two approaches, numerical methods for solving three surface problems are proposed: 1) minimal surface problems, in which the form that minimizes the mean curvature was computed by iterative update of a level-set function discretized using TraceFEM and driven by advection, for which the velocity field was given by the mean curvature flow, 2) elastic membrane problems discretized using linear and higher order TraceFEM, which makes it straightforward to embed complex geometries of membrane models into an elastic bulk for reinforcement and 3) stabilized, accurate vertex normal and mean curvature estimation with local refinement on triangulated surfaces. In this thesis the basics of the two main approaches are presented, some aspects such as stabilization and surface reconstruction are further developed, evaluated and numerically analyzed, details on implementations are provided and the current state of work is presented.

sted, utgiver, år, opplag, sider
Jönköping: Jönköping University, School of Engineering, 2017. s. 144
Serie
JTH Dissertation Series ; 022
Emneord
trace finite element method, membrane, mean curvature, level-set method
HSV kategori
Identifikatorer
urn:nbn:se:hj:diva-35369 (URN)978-91-87289-23-1 (ISBN)
Disputas
2017-05-12, E1405, Tekniska Högskolan, Jönköping, 10:00 (engelsk)
Opponent
Veileder
Forskningsfinansiär
Swedish Research Council, 2011-4992
Tilgjengelig fra: 2017-04-13 Laget: 2017-04-13 Sist oppdatert: 2018-08-17bibliografisk kontrollert

Open Access i DiVA

fulltext(21844 kB)55 nedlastinger
Filinformasjon
Fil FULLTEXT01.pdfFilstørrelse 21844 kBChecksum SHA-512
4ad7d219ed474c3ef9ad540aeacf4e33ab376602f68491c248b1a495e5e0cc8afa416f3162b7b1dd85c742a1e86c508c30f5534bebea8faf2c38a865285c41fa
Type fulltextMimetype application/pdf

Andre lenker

Forlagets fulltekstScopus

Personposter BETA

Cenanovic, MirzaHansbo, Peter

Søk i DiVA

Av forfatter/redaktør
Cenanovic, MirzaHansbo, Peter
Av organisasjonen
I samme tidsskrift
Computer Methods in Applied Mechanics and Engineering

Søk utenfor DiVA

GoogleGoogle Scholar
Totalt: 55 nedlastinger
Antall nedlastinger er summen av alle nedlastinger av alle fulltekster. Det kan for eksempel være tidligere versjoner som er ikke lenger tilgjengelige

doi
urn-nbn

Altmetric

doi
urn-nbn
Totalt: 487 treff
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf