A generalized finite element method for linear thermoelasticity
Licentiatavhandling, 2016

In this thesis we develop a generalized finite element method for linear thermoelasticity problems, modeling displacement and temperature in an elastic body. We focus on strongly heterogeneous materials, like composites. For classical finite element methods such problems are known to be numerically challenging due to the rapid variations in the data. The method we propose is based on the local orthogonal decomposition technique introduced by M{\aa}lqvist and Peterseim (Math. Comp., 83(290): 2583--2603, 2014). In short, the idea is to enrich the classical finite element nodal basis function using information from the diffusion coefficient. Locally, these basis functions have better approximation properties than the nodal basis functions. The papers included in this thesis first extends the local orthogonal decomposition framework to parabolic problems (Paper I) and to linear elasticity equations (Paper II). Finally, using the theory developed in these papers, we address the linear thermoelastic system (Paper III).

a priori analysis

Thermoelasticity

linear elasticity

generalized finite element

parabolic equations

local orthogonal decomposition

composites

multiscale

Euler
Opponent: Daniel Peterseim

Författare

Anna Persson

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Multiscale techniques for parabolic equations

Numerische Mathematik,; Vol. 138(2018)p. 191-217

Artikel i vetenskaplig tidskrift

A multiscale method for linear elasticity reducing Poisson locking

Computer Methods in Applied Mechanics and Engineering,; Vol. 310(2016)p. 156-171

Artikel i vetenskaplig tidskrift

A Generalized Finite Element Method for Linear Thermoelasticity

Mathematical Modelling and Numerical Analysis,; Vol. 51(2017)p. 1145-1171

Artikel i vetenskaplig tidskrift

Ämneskategorier

Beräkningsmatematik

Utgivare

Chalmers tekniska högskola

Euler

Opponent: Daniel Peterseim

Mer information

Senast uppdaterat

2020-02-03