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A generalized finite element method for linear thermoelasticity

Anna Persson (Institutionen för matematiska vetenskaper)
Göteborg : Chalmers University of Technology, 2016. - 118 s.
[Licentiatavhandling]

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).

Nyckelord: Thermoelasticity, parabolic equations, linear elasticity, multiscale, composites, generalized finite element, local orthogonal decomposition, a priori analysis



Denna post skapades 2016-05-02. Senast ändrad 2016-05-11.
CPL Pubid: 235750

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)

Ämnesområden

Numerisk analys

Chalmers infrastruktur

Examination

Datum: 2016-05-27
Tid: 10:15
Lokal: Euler
Opponent: Daniel Peterseim