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- Larsson, Karl,1981-Umeå universitet,Institutionen för matematik och matematisk statistik,UMIT (author)
Finite Element Methods for Thin Structures with Applications in Solid Mechanics
- BookEnglish2013
Publisher, publication year, extent ...
- Umeå :Umeå universitet,2013
- vi, 18 s.
- electronicrdacarrier
Numbers
- LIBRIS-ID:oai:DiVA.org:umu-79297
- ISBN:9789174596533
- ISBN:9789174596540
- https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-79297URI
Supplementary language notes
- Language:English
- Summary in:English
Part of subdatabase
- SwePubSwePub
Classification
Series
- Doctoral thesis / Umeå University, Department of Mathematics,1102-8300 ;54
Notes
- 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 L2-norm and provide numerical results to support our findings.The third paper deals with the biharmonic equation on a surface embedded in R3. 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 L2-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 R3. 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.
Subject headings and genre
- NATURVETENSKAP Matematik Beräkningsmatematik hsv//swe
- NATURAL SCIENCES Mathematics Computational Mathematics hsv//eng
- a priori error estimation
- finite element method
- discontinuous Galerkin
- corotation
- Kirchhoff-Love plate
- curved beam
- biharmonic equation
- Mathematics
- matematik
Added entries (persons, corporate bodies, meetings, titles ...)
- Larson, Mats G,ProfessorUmeå universitet,Institutionen för matematik och matematisk statistik(Swepub:umu)mala0002 (thesis advisor)
- Wells, Garth N,ReaderDepartment of Engineering, University of Cambridge (opponent)
- Umeå universitetInstitutionen för matematik och matematisk statistik (creator_code:org_t)
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