Augmented Beam Elements Using Unit De ection Shapes Together with a Finite Element Discretisation of the Cross Section
Translated title:
Augmented Beam Elements Using Unit De ection Shapes Together with a Finite Element Discretisation of the Cross Section
Author:
Kreutz, Johannes
Document type:
Dissertation
Faculty/School:
Ingenieurfakultät Bau Geo Umwelt
Advisor:
Univ.-Prof. Dr.-Ing. habil. G. H. Müller
Referee:
Univ.-Prof. Dr.techn. Chr. Adam
Language:
de
Subject group:
BAU Bauingenieurwesen, Vermessungswesen
TUM classification:
BAU 150d
Abstract:
This thesis covers the eld of augmented beam Finite Elements for geometrical and material
linear, prismatic structures in the elds of static and dynamic excitations. An approach of
superposed unit de
ection shapes which are de ned on a two dimensional Finite Element
mesh of the cross section is used. This Finite Element mesh of the cross section is also used
for the preparation of the unit de
ection shapes by solving di erent di erential equations
such that unit de
ection shapes emerge which most e ectively cover the physical e ects
occurring on beam shaped structures with a three dimensional material law. The concept of
unit de
ection shapes is in analogy with the concept of warping torsion of beam elements.
The method is validated and visualised with several numerical examples which are compared
to the results of three dimensional standard Finite Element models.
«
This thesis covers the eld of augmented beam Finite Elements for geometrical and material
linear, prismatic structures in the elds of static and dynamic excitations. An approach of
superposed unit de
ection shapes which are de ned on a two dimensional Finite Element
mesh of the cross section is used. This Finite Element mesh of the cross section is also used
for the preparation of the unit de
ection shapes by solving di erent di erential equations
such that unit de
ection shapes emerge...
»
Translated abstract:
This thesis covers the eld of augmented beam Finite Elements for geometrical and material
linear, prismatic structures in the elds of static and dynamic excitations. An approach of
superposed unit de
ection shapes which are de ned on a two dimensional Finite Element
mesh of the cross section is used. This Finite Element mesh of the cross section is also used
for the preparation of the unit de
ection shapes by solving di erent di erential equations
such that unit de
ection shapes emerge which most e ectively cover the physical e ects
occurring on beam shaped structures with a three dimensional material law. The concept of
unit de
ection shapes is in analogy with the concept of warping torsion of beam elements.
The method is validated and visualised with several numerical examples which are compared
to the results of three dimensional standard Finite Element models.
«
This thesis covers the eld of augmented beam Finite Elements for geometrical and material
linear, prismatic structures in the elds of static and dynamic excitations. An approach of
superposed unit de
ection shapes which are de ned on a two dimensional Finite Element
mesh of the cross section is used. This Finite Element mesh of the cross section is also used
for the preparation of the unit de
ection shapes by solving di erent di erential equations
such that unit de
ection shapes emerge...
»
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