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**Harvard**

Oddy, C. och Bisschop, R. (2017) *Multiscale modelling of heterogeneous beams*. Göteborg : Chalmers University of Technology (Diploma work - Department of Applied Mechanics, Chalmers University of Technology, Göteborg, Sweden, nr: 2017:46).

** BibTeX **

@mastersthesis{

Oddy2017,

author={Oddy, Carolyn and Bisschop, Roeland},

title={Multiscale modelling of heterogeneous beams},

abstract={Material heterogeneities, such as pores, inclusion or manufacturing defects can have a detrimental impact
on the performance of structural components, such as beams, plates and shells. These heterogeneities are
typically dened on a much ner scale than that of the structural component, meaning that fully resolving
the substructure in numerical analyses is computationally expensive. A method known as FE2 is therefore
considered. As the name suggests, it links at least two nite element (FE) analyses, one dening the macroscale,
the other the subscale, in a nested solution procedure. Of particular interest however, are the prolongation
(macro-subscale) and homogenisation (subscale-macroscale) techniques used to link a macroscale beam to a
statistical volume element (SVE), used to characterise the subscale.
Multiple prolongation and homogenisation methods are presented. Although capturing an accurate elongation
and bending response is straightforward, the same cannot be said for the shear response. The standard use of
Dirichlet, Neumann, and periodic boundary conditions is insucient. As the length of a statistical volume
element (SVE) increases, there is a deterioration in geometric behaviour. More specically, the SVE begins to
bend in an unphysically manner, leading to overly soft results.
Variationally Consistent Homogenisation (VCH), provides a systematic way to formulate the macroscale and
subscale problem, as well as the link between them. Through the introduction of VCH, an additional volumetric
constraints, which imposes an internal rotation, is formulated. The additional constraint provides a drastic
improvement. The degradation in shear behaviour is no longer apparent and an accurate shear response is
captured. It is important to note however, that this is not an ideal solution, as adding the volumetric constraint
perturbs the physicality of the subscale problem.
Keywords: Beams, heterogeneities, homogenisation, prolongation},

publisher={Institutionen för tillämpad mekanik, Material- och beräkningsmekanik, Chalmers tekniska högskola},

place={Göteborg},

year={2017},

series={Diploma work - Department of Applied Mechanics, Chalmers University of Technology, Göteborg, Sweden, no: 2017:46},

}

** RefWorks **

RT Generic

SR Electronic

ID 250370

A1 Oddy, Carolyn

A1 Bisschop, Roeland

T1 Multiscale modelling of heterogeneous beams

YR 2017

AB Material heterogeneities, such as pores, inclusion or manufacturing defects can have a detrimental impact
on the performance of structural components, such as beams, plates and shells. These heterogeneities are
typically dened on a much ner scale than that of the structural component, meaning that fully resolving
the substructure in numerical analyses is computationally expensive. A method known as FE2 is therefore
considered. As the name suggests, it links at least two nite element (FE) analyses, one dening the macroscale,
the other the subscale, in a nested solution procedure. Of particular interest however, are the prolongation
(macro-subscale) and homogenisation (subscale-macroscale) techniques used to link a macroscale beam to a
statistical volume element (SVE), used to characterise the subscale.
Multiple prolongation and homogenisation methods are presented. Although capturing an accurate elongation
and bending response is straightforward, the same cannot be said for the shear response. The standard use of
Dirichlet, Neumann, and periodic boundary conditions is insucient. As the length of a statistical volume
element (SVE) increases, there is a deterioration in geometric behaviour. More specically, the SVE begins to
bend in an unphysically manner, leading to overly soft results.
Variationally Consistent Homogenisation (VCH), provides a systematic way to formulate the macroscale and
subscale problem, as well as the link between them. Through the introduction of VCH, an additional volumetric
constraints, which imposes an internal rotation, is formulated. The additional constraint provides a drastic
improvement. The degradation in shear behaviour is no longer apparent and an accurate shear response is
captured. It is important to note however, that this is not an ideal solution, as adding the volumetric constraint
perturbs the physicality of the subscale problem.
Keywords: Beams, heterogeneities, homogenisation, prolongation

PB Institutionen för tillämpad mekanik, Material- och beräkningsmekanik, Chalmers tekniska högskola,PB Institutionen för tillämpad mekanik, Material- och beräkningsmekanik, Chalmers tekniska högskola,

T3 Diploma work - Department of Applied Mechanics, Chalmers University of Technology, Göteborg, Sweden, no: 2017:46

LA eng

LK http://publications.lib.chalmers.se/records/fulltext/250370/250370.pdf

OL 30