Department o
of Civil Engine
eering and Surrveying
Institute of Me
ethodological Fundamentals
s in Civil Engi neering
Chair of Strucctural Mechan
nics
Dissertatio
on Fact Sh
heet
Develop
pment off Macro-E
Elements
s in Half--Space Dynamics
D
s Using the
t
Bounda
ary Eleme
ent Meth
hod and tthe Integ
gral Transformatiion Meth
hod
Na
ame
Martin Den
ngler M.Sc.
E--Mail
martin.den [email protected]
m.de
Su
upervisor
Univ.-Prof. Dr. Gerhard
d Müller
Chair of St ructural Mechanics
Sttarted
03/2011
Sttatus
ongoing
g
Dynamic loa
ads on the building
b
groun
nd cause gro
ound
vibrations w
which can lead to imp
pairment off the
service abillity of buildin
ngs. The pre
ediction of th
hese
vibrations in practice
e is usua
ally based on
measureme
ents or simp
ple engineerring approacches
which are lim
mited in their accuracy.
A treatmentt of the prob
blem with ana
alytical meth
hods,
such as the
e Integral Transformatio
on Method o
or by
numerical methods su
uch as the Finite Elem
ment
Method or Boundary Element
E
Method provide
es a
more accurrate predictio
on of the viibrations, ass the
above menttioned engine
eering appro
oaches.
finaliz
zed:
thre
ee-time Fourier Transfoormation. Fo
or these in
n
simple geomettries, closedd form so
olutions are
e
available. With this
t
method the solution can be splitt
in near
n
fields an
nd far fields with a large
e penetration
n
dep
pth. Because of its rapid ddecay, near fields do nott
have to be cons
sidered in thhe boundary
y integrals off
morre distant edges. Thiis approach
h allows a
redu
uction of the computationnal effort in applying the
e
Bou
undary Eleme
ent Method.
By combining the Boundary Eleme
ent Method with
the Integral Transformation Method, the advanta
ages
of both metthods can be
e exploited. With
W the Inte
egral
Transformation Method
d, closed form solutionss for
simple geom
metries can be
b found, wh
hile the Boun
ndary
Element Me
ethod provides approxim
mate solution s for
arbitrary geometries.
In the conte
ext of this th
hesis the numerical efforrt for
computing infinite syste
ems with bou
undary elem
ments
shall be re
educed by using
u
global shape funcction
from the In
ntegral Transformation Method.
M
Forr the
epending on
boundary de
n its geometrry, global or local
shape funcctions are applied.
a
Regular edgess as
straight-, cyylindrical- (3D
D) or circularr boundariess can
be discretized with global
g
shap
pe functionss, at
irregular boundaries loccal shape functions are u
used
(Fig.1). The
e description
n by global shape functtions
requires th
he knowledg
ge of furth
her fundame
ental
solutions, w
which can be
e determined
d by the Inte
egral
Transformation
Meth
hod.
Therrefore
La mé's
differential equation, which
w
is a system
s
of tthree
coupled partial differen
ntial equation
ns, is decou
upled
with the help of the Helm
mholtz decom
mposition. O
Out of
these parrtial differe
ential equa
ations, ordiinary
differential equations are
a obtained
d by applyin
ng a
Fig. 1: Discretiz
zation of the boundary off a halfspace with
w circular aand rectangu
ular cavity
Refferences
Mülller, G. (1993): Ein Verfahrenn zur Kopplun
ng der
Randelementmeth
hode mit analyytischen Lösungsansätzen,
TU München,
M
Hab
bilitation.
Früh
he, G. (2011): Überlagerungg von Grundlösungen in derr
Elas
stodynamik zur Behandlungg der dynamisc
chen TunnelBod
den-Bauwerk-In
nteraktion, TU
U München, Diissertation.