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DOCTORAL SCHOOL: CIVIL ENGINEERING Research within the field of civil engineering is concerned with the
scientific and technological aspects of manmade changes of the physical
environment, including the following specialist fields: ·
Structural Analysis and Design. ·
Materials Science. ·
Indoor Environmental Technology. ·
Information and Communication Technology (ICT) in the
Building Process ·
Marine Civil Engineering and Environmental Hydraulics. ·
Soil Mechanics. ·
Structural Dynamics and Mechanics ·
Geographical Information Systems (GIS). ·
Digital Cartography. ·
Global Navigation Satellite Systems (GNSS). Plants
and structures, where the above fields are used, include e.g. buildings,
masts, transport facilities (roads, bridges, railways, harbours, tunnels,
canals, locks, etc.), sanitary engineering plants (water supply, urban
drains and sewage disposal, etc.), offshore structures (oil and gas
exploitation and transport), wind turbines, hydroelectric structures and
plants for irrigation, drainage and coastal protection. The environmental
aspects of these are also included in the relevant specialist fields. The physical environment is mapped using land surveying and
photogrammetry, and geographical information (statutory, economic,
sociological, landuse, environmental and resource utilization, spatial
or descriptive) is displayed cartographically or stored as computerized
geodata. The PhD programme in Civil Engineering is organized in the following
departments: ·
The Department of Civil Engineering. ·
The Department of Development and Planning. The programme provides for
specialization in the following: ·
The Department of Civil Engineering:
o
Air flow in rooms. o
Industrial ventilation. o
Control strategies and energy conversion in buildings. o
Structural reliability theory and risk analysis. o
Computational mechanics. o
Structural design. o
Virtual building models o
User environment and ICT-supported collaboration o
Knowledge management and transfer o
Structural materials. o
Experimental mechanics. o
Wave hydraulics and modelling.Loads on fixed and
floating coastal and offshore structures. o
Reliable design of coastal and harbour structures. o
Numerical modelling of flow and water quality. o
Dynamics of settling tanks, process tanks and
sedimentation basins. o
Groundwater flow and pollution transport. o
Pollution transport in natural waters. o
Urban drainage and sewage systems. o
Strength and deformation of different soil types. o
Soil dynamics. o
Wave transmission in soils. o
Hydrogeology. o
Fluid-Structure Interaction. o
Soil-Structure Interaction. o
Building Acoustics. o
Experimental Dynamics. The
Department of Development and Planning: o
Geographical information systems (GIS) and digital
cartography. o
Global Navigation Satellite Systems (GNSS). I. Department of Civil Engineering The
Department of Civil Engineering focuses on the fields which form the
scientific and technological basis for development within the field of
building technology, including structures and the technical installations
for housing, commercial and industrial buildings, bridges and other civil
engineering structures. The PhD programme is organized in the research
environments for Indoor Environmental Technology, Structural Analysis and
Structural Design, Marine civil engineering and environmental hydraulics,
Soil mechanics and Structural Dynamics and Mechanics Indoor Environmental Technology offers the following
fields of research: Air
flow in rooms
is concerned with the methods of creating thermal comfort and high air
quality for persons and animals. A major field is the selection of
materials and composition of the building envelope, as well as the choice
of appropriate heating and ventilation installations. Different principles
of heating and ventilation are analysed, and full-scale models or small
scale models are made according to the individual tasks. Analytical models
are used, based on integrated descriptions of flow elements, as well as
computational fluid dynamics models based on finite volume description of
the air flow. Elements of flow fields in a room are studied, and thermal
manikins can be used for the simulation of persons in a room. Contact person: Industrial ventilation is concerned with the methods of creating the optimal
thermal conditions in industrial environments, and to protect persons from
the influences of processes emitting harmful substances. The elements of
flow in different contaminating processes are examined by model and full-scale
experiments, as well as by means of the numerical simulation of air flow
and gas and particle transport. A boundary condition description is
developed for different contaminating processes for use in the numerical
simulation of gas and particle transport. Optimization of different
solutions based on air movement for protection of people as e.g. local
exhaust is studied. Contact person: Control strategies and energy conversion in buildings
concerns methods to analyse and calculate energy conversion in buildings,
in various components, and in complete heating and ventilation systems
under dynamic load conditions. This includes the development and testing
of strategies for a more consciously controlled consumption of energy
resources. System identification and parameter estimation are studied, and
computer models, modified by the knowledge gained from the study of air
distribution in rooms, are developed. Contact person: Mogens Steen-Thøde, associate professor; e-mail: m44mst@aub.aau.dk
Structural Analysis offers the following fields of
research: Structural
reliability theory
is concerned with the methods of modelling uncertainty in relation to
structural design, and rational methods to assess the reliability of
designs based on statistical knowledge of loads and strengths. These methods are an important element in decision and risk analysis of
problems in relation to structural design, e.g. optimal design, inspection
planning and the selection of optimal repair and maintenance strategies
for bridges, wind turbines, offshore structures, etc. Contact persons: Computational Mechanics is concerned with development of models and the
related computational methods, algorithms and computer programmes for
problems within solid and structural mechanics. Stability problems and
constitutive models, e.g. in the form of plasticity theory for steel,
concrete and soils are studied. Computational algorithms are developed for
eigenvalue analysis and solution of strongly nonlinear equations arising
in finite element analysis. Contact person: Esben Byskov, professor; e-mail: esben@bt.aau.dk
Materials mechanics: Material Mechanics is concerned with the analysis of
phenomena such as fracture, plasticity and strain localization. Both the
development of fundamental concepts and analyses of specific phenomena are
of interest. Examples include i) the development of interface fracture
criteria which takes the morphology of the interface and plastic
deformation at the crack tips into account, ii) the development of
nonlinear constitutive relations for fiber composites, iii) the modeling
of strain localization (kink bands) in fiber composites due to interaction
between plasticity of the matrix material and micro buckling of the
fibers, iv) the development of computational methods for studying the
propagation of interface cracks in adhesive joints based on fracture
mechanics and cohesive zone models, v) delamination of layers and coatings
due to external loads and residual stresses. Contact person: Structural Design offers the following fields of
research: ICT
in the Building Process
at
Contact persons: User Environment Design and ICT-supported
Collaboration:
The Internet and www based ICT tools provide us with possibilities to
creatively design, implement, and usability evaluate new user environments
for collaboration and adapted access of ICT tools. Research focus is on
end user needs capture and requirements formulation, user environments
design and prototyping in coordination with ICT tools implementation, and
multimedia and virtual reality access to building product and process
models. Contact persons: Knowledge
Management and Transfer Today
most of the information we produce is stored digitally. We are slowly
forced to leave behind us thinking about information as something stored
in physical containers as books, drawings etc but dynamically filtered and
accessed in www based distributed information containers. Research focus
is on use of mixed knowledge representations to support collaboration and
knowledge transfer, knowledge management services using emerging Semantic
Web technologies as well as industry university knowledge transfer and
learning systems. Contact persons: Structural Materials includes, primarily, the field of material physics and
material mechanics and the durability properties of building materials. It
includes formulation of theories and models for the behaviour of materials,
in production and in use. The theoretical treatment can begin with the
microstructure of materials or with macro considerations specific for
individual materials, e.g., fracture and durability. An important research
field is the development and design of new materials, especially fibre
reinforced concrete and high strength concrete. Contact person: Eigil V. Sørensen, associate professor; e-mail: evs@bt.aau.dk
Experimental Mechanics is a field, in which information is sought on the
behaviour of materials and structures by means of observation. It covers
experimental mechanics and experimental fire precaution technology, and
includes, e.g., theory for model laws, methods for the optimal planning of
experiments, methods for observation by means of analogue and digital
equipment, data acquisition instruments and methods for processing data,
including system identification. Contact person: Peter Ellegaard, associate professor; e-mail: pe@bt.aau.dk
Marine Civil Engineering and Environmental Hydraulics Marine
civil engineering and environmental hydraulics contains the engineering
aspects of hydraulics (pipe and channel hydraulics, wave hydraulics,
hydrology, harbour construction, coast protection, offshore technology,
recipient hydraulics, drains, sewage treatment and disposal technology,
water supply and irrigation and drainage. The laboratory contains three
hydraulic channels, two wave channels and two wave basins for two and
three dimensional waves and equipment for field investigations. Marine civil engineering and environmental hydraulics offers studies
within the following fields of research, and studies are also offered for
combined hydraulic and environmental problem concepts. Please see also the
Wave hydraulics, physical and numerical modelling
is a basic research field in relation to construction and design in the
sea and along coasts. Wind generated waves are the main cause of loading
on most stationary and floating structures in the marine environment.
Numerical methods are becoming much more used in the calculation of wave
fields in coastal areas and in harbours, since there are effective
numerical methods for the determination of nonlinear wave fields.
Research is concentrated on physical wave generation and the analysis of
anomalous two and three dimensional waves, on the development of
techniques and computer programmes to generate waves in the laboratory
test basins, and on the development of effective numerical methods for the
determination of these nonlinear wave fields. Contact persons: Hans F. Burcharth, professor; e-mail: i5hfb@civil.aau.dk,
Michael Brorsen, associate professor; e-mail: i5mb@civil.aau.dk,
and Peter Frigaard, associate professor; e-mail: peter.frigaard@civil.aau.dk
Loads on fixed and floating coastal and offshore structures:
wave loading is the most frequent determination for the design and economy
of marine structures. However, uncertainty about the determination of wave loading and the
related structural response is often great. Nonlinear wave loading is
often the cause of great movement in floating structures because of a
considerable dynamic increase. Research is concentrated on experimental examinations and theoretical
analysis of loading from two and three dimensional waves, primarily on
breakwaters, piers and jetties, coastal protection structures and offshore
structures. For the floating structures the research is concentrated on
the development of numerical methods for the determination of the so-called
operational forces, i.e. slow variation of loads, and the related
movements. Contact persons: Hans F. Burcharth, professor; e-mail: i5hfb@civil.aau.dk,
and Michael Brorsen, associate professor; e-mail: i5mb@civil.aau.dk
Reliability based design of coastal and harbour structures:
There is a growing requirement for more reliable and economic coastal and
harbour structures. Research is being carried out within the following fields which,
collectively, provide a synthesis in relation to the design process: ·
Methods for the determination of measurable wave
conditions in consideration of uncertainties and levels of structural
safety. ·
Theoretical and experimental examinations of types of
failure in pier and coastal protection structures. ·
Development of quantification methods based on
reliability theories. Contact
person: Hans F. Burcharth, professor; e-mail: i5hfb@civil.aau.dk Numerical modelling of flow and water quality:
Despite a considerable political and economic contribution in recent
decades, the pollution of Danish watercourses, lakes, fiords and seas is
still significant. An important element in the assessment of the
improvement, which the present and future operation will have on that
situation, will be the numerical hydraulic models. By means of these, the
flow of water under different conditions can be simulated, after which
simulation with numerical models for the transport of both solutions and
particles, distribution and transformation, in the currents, can be used
in the assessment of the effect of an operation. Research activities in
this field, are often implemented in a cooperation with the laboratory
of environmental engineering. Contact person: Kjeld Schaarup-Jensen, associate professor; e-mail: i5ksj@civil.aau.dk
Dynamics of settling tanks, process tanks and sedimentation basins:
Flow and transport of particles in a number of technical installations
like settling tanks, process tanks, sedimentation basins, is a field which
has been of growing importance in recent decades. In the suspension phase,
in transport, particles will normally flocculate into larger aggregates,
and they will bind together to form an erosion resistant cohesive
sediment when deposited on the bottom. In high concentrations, the
suspended materials can display non-Newtonian properties, i.e. form a
transition between liquid and solid state which has a finite displacement
strength. Contact person: Torben Larsen, professor; e-mail: i5tl@civil.aau.dk
Groundwater flow and pollution transport:
The volume and quality of groundwater resources are the starting point for
water supply. The exploitation of agricultural areas and the earlier
practices of dumping waste materials have created many possibilities for
pollution of the natural groundwater resources. PhD projects on
groundwater topics will include hydraulics and transport of solubles in
the unsaturated and saturated zones. Contact person: Kjeld Schaarup-Jensen, associate professor; e-mail: i5ksj@civil.aau.dk Pollution transport in natural waters:
The transport of sewage and polluted surface runoff or polluted
groundwater to natural waters like watercourses, lakes and marine
environments is important to the design and localization of a number of
technical installations. A forecast of the transport and distribution of
the discharged substances is necessary. Projects in this field are
concerned with the study of local three dimensional conditions, and also
one and two dimensional conditions on a larger scale, e.g. an estuary or
sea area. Contact person: Torben Larsen, professor; e-mail: i5tl@civil.aau.dk Urban drainage and sewer sediment transport:
Urban hydrology and hydraulics and material transport in drainage and
sewage systems are central elements of the urban infrastructure. The
improvement of existing systems and new replacements aimed at limiting the
extent of pollution, e.g. by establishing storm drainage storage basins,
will become important tasks in the decades of the near future. Projects in
this field will include the interaction between hydraulic conditions,
sediment transport and water quality. Contact persons: Kjeld Schaarup-Jensen, associate professor; e-mail: i5ksj@civil.aau.dk,
and Torben Larsen, professor; e-mail: i5tl@civil.aau.dk Soil Mechanics Soil
Mechanics is concerned with the engineering problem concepts connected
with the transfer of forces from structures to the soil (buildings,
bridges, roads, retaining walls, quays), and with the use of soil as
building material (embankments, dikes, piers). It includes such fields as:
Engineering geology, soil mechanics, soil dynamics, hydrology and
submarine soil mechanics. The laboratory contains the traditional
measuring equipment for soil mechanics, and also equipment for dynamic
experiments and hydraulic experiments. Furthermore, the research
environment include an experimental testing room with extensive facilities
for the construction of different models. Soil Mechanics offers studies
within the following fields of research: Strength and deformation of characteristic soil types:
This is fundamental for soil mechanics. The constant development of more
advanced calculation facilities, e.g. element method computer programmes,
has increased the demand for precision in the models used to describe the
strength and deformation properties of soils. It has long been a desire to
be able to explore the behaviour of soil elements under truly triaxial
conditions, which is now possible by means of the laboratory's cubic
compression apparatus. Contact person: Carsten S. Sørensen, associate professor; e-mail: i5css@civil.aau.dk
Soil dynamics: The sensitiveness of types of soils to the building
up of pore pressure with varying loads is a problem, which plays an
important role, e.g. in the assessment of stability and safety in many
offshore structures. Research into the behaviour of many soil types under
these conditions have begun in the laboratory, but there is a need to
continue with the studies and tests for fatigue by means of models. Contact person: Lars Andersen, associate professor; e-mail: i5la@civil.aau.dk
Wave transmission in soils: The properties of types of soils to transmit or brake
pressure or sound waves play an important role in different relationships,
e.g. the assessment of risk conditions with earthquakes, the risks of
damage with pile driving, and the interpretation of seismic signals in
connection with geological mapping. The focus is on field experiments and
resonance column experiments in the laboratory. Contact person: Lars Andersen, associate professor; e-mail: i5la@civil.aau.dk Structural
Dynamics and Mechanics Fluid Structure Interaction:
As structures such as wind turbines, suspension bridges and shell
structures become larger without a proportional increase of stiffness, the
structures become increasingly prone to various kinds of aeroelastic
instability and buffeting induced vibrations from the wind. The aim is to
investigate these phenomena by means of a complete 3D modelling of fluid
and structure. Especially, the influence of turbulence, 3D-separation
patterns (e.g. dynamic stall) and reattachments of boundary layers are
studied. Contact
persons: Niels N. Sørensen, professor and Nonlinear Multibody Dynamics of Wind Turbines:
The
multibody modelling principle implies that each substructure of a wind
turbine, such as tower, nacelle, transmission system, and wings, are
modelled independent, and linked together via algebraic constraints. The
idea is to model each wing in a rotating coordinate system in which case
the influence of non-linearities become rather small. The modelling is
performed based on a co-rotating beamelement formulation with the rotating
coordinate system as the frame of reference. The algebraic couplings
between the various substructures induce infinite stiffness components,
and hence infinite eigenfrequencies, in the global dynamic system. This
may compromise usual numerical time integrators. A substantial part of the
project deals with the devise of numerical time integrators to deal with
this problem. Especially, the idea is to develop energy conserving
algorithms, which at the same time conserve momentum and moment of
momentum of the timediscretized system. Additionally, the project deals
with the development of suitable system reduction schemes for geometrical
nonlinear substructures. The aim is to implement the integrated system in
an active vibration control algorithm for a wind turbine, which
necessitates real time analysis of the structural model of the wind
turbine. Contact
person: Søren R.K. Nielsen, professor; e-mail: soren.nielsen@civil.aau.dk
Active, Semiactive, Passive and Smart Material
Strategies for Vibration Control of Wind Turbines:
Due to increasing problems with deflections of tower and wings it
is necessary to have a control strategy to reduce excessive vibrations.
Basically, the pitch actuators at the hub may be used to generate an
aerodynamic control force on the wings. Similarly, the generator torque
may be used to reduce edgewise vibrations of the blades and vibrations in
the transmission system. Alternatively, piezoelectric and SMA materials
have been investigated for use as actuators of the aerodynamic control
loads. The idea is to twist the outher part of the wings by means of these
actuators in order to avoid the acceleration of the majority of the mass
of the wing in the vicinity of the hub, which part of the wing is not
contributing to the aerodynamic control force. Further, various
semiactive control strategies for reduction of tower vibrations have been
investigated (based on rheological MR and ER dampers). In any case the
dynamics of the control systems are integrated with a real time processing
of a structural dynamic model of the wind turbine. Contact
person: Søren R.K. Nielsen, professor; e-mail: soren.nielsen@civil.aau.dk Stochastic Response of Shallow Cables:
Shallow
cable systems are used to supply support and stability to cable stayed
bridges, masts and TV-towers. The primary external excitation of such
cables is caused by the motion of the support points of the cable rather
than by dynamic wind or aeroelastic loads. An important effect of
the support motion is the timevariation of the chord in the equilibrium
suspension, which causes parametric excitation of the modal equations of
motions. Further, the response is prone to geometrical nonlinearities.
Traditionally, the response of shallow cables have been restricted to
harmonically varying support point motions. However, in reality the
excitation is better described by a narrowbanded stochastic process with a
center frequency reflecting the fundamental eigenfrequency of the global
structure. Under harmonically stochastic excitation, where the
centerfrequency of the excitation is close to the fundamental
eigenfrequency of the cable, the response is jumping between various
periodic attractors as the the envelope of the excitation process is
varying. Under subharmonic stochastic excitation of order 2, where the
center frequency is close to twice the fundamental eigenfrequency, the
response is quantitatively and qualitatively different from the harmonic
deterministic case even for extreme narrowbandedness of the excitation.
Further, chaotic stochastic response (as detected by a numerical
determined Lyapunov exponent) may occur dependent on the variance of
the excitation process. Similar investigations have been performed for
other orders of subharmonic and superharmonic stochastic excitation. Contact
person: Søren R.K. Nielsen, professor; e-mail: soren.nielsen@civil.aau.dk III. The Department of Development and Planning: Mapping
and information systems includes research fields like mapping,
geographical information systems, land surveying, photogrammetry,
cartography, engineering survey and remote sensing. They consist of the
theories and methods for the collection, calculation and presentation of
spatial data, as well as their application in other technical fields. PhD
programmes are offered in the following: Digital cartography: Digital cartography includes the testing of manual and automatic methods
for the collection, structuring, storing, exchanging, generalizing,
updating and presentation of point, vector and scanned surface data. The
methods can be from land surveying, photogrammetry and image processing,
or cartography. Current topics are the production of digital
orthophotomaps and digital terrain models, and their application,
automatic measurement and object recognition in digital photographs,
online data collection in land surveying, computer supported
generalization and the design of new types of maps. Contact person: Peter Cederholm, associate professor;
e-mail: pce@land.aau.dk Global Navigation Satellite
Systems (GNSS): GPS is an important technology in the fields of
surveying, mapping, and GIS. Relative positioning techniquies produce real
time accuracies at the centimetre level or even subcentimetre level.
Research is partly focused on GPS as a stand-alone tool for surveying, and
partly on combining GPS with other sensors. Contact person: Peter Cederholm, associate professor;
e-mail: pce@land.aau.dk Subject oriented PhD-course study programme courses are
offered on the following topics: Advanced Mathematical Methods in (Classical) Linear Elasticity The
course utilizes advanced mathematical methods, particularly complex
function theory, to develop general solutions to problems in linear
elasticity. The concept of analytic functions, the Cauchy-Riemann
equations, analytic continuation, and conformal mappings will be presented.
The method of Muskhelishvili will be utilized to cast the general
solutions of two-dimensional linear elasticity problems within the
framework of complex function theory. Solutions
to specific boundary value problems will be obtained. These include
problems defined in cylindrical regions, cylindrical cavities,
dislocations, cracks and on the half plane. Solutions to the anti-plane
problems of linear elasticity will be obtained. Some general solutions to
the three-dimensional problems in linear elasticity will be developed if
time permits. Duration: 3 ECTS. Non-Linear Modelling and Analysis of Structures and Solids An increasing number of problems in solid and
structural mechanics require the use of non-linear models due to geometric
or material non-linearities. The use of non-linear analysis requires
knowledge of the underlying models as well as of appropriate numerical
solution techniques. It is the goal of the course to present the basic
theory behind non-linear deformation due to large displacements and
rotations, and to give an introduction to some of the basic features of
non-linear material models. The course includes classic exercises on
theory as well as hands-on work with simple numerical examples, based on
prepared MATLAB subroutines. The course consists of six full days of
combined lectures and exercises. The subjects covered are: Introduction to
the structure of non-linearity in analysis of structures and solids,
Development of exact theories for truss structures to illustrate general
techniques in a simple setting, The theory of finite rotations – how to
describe, combine and manipulate structures in space, Fully non-linear
theory for elastic beams with large rotations, The co-rotational element
concept illustrated with beam elements in two and three dimensions, Basic
non-linear continuum mechanics, the different strain measures, the
corresponding stresses, and the material rate of change of stresses, The
fundamental structure of plasticity theory, classic metal plasticity and
the associated algorithms for numerical solution, Plasticity models of
soils and friction materials, Numerical solution techniques for tracing
non-linear load-response paths dynamic effects and some associated
numerical solution techniques. Duration: 3.5 ECTS. Modelling Natural and
Hybrid Ventilation The
objective of the course is to introduce and apply the theoretical
background and methods for single and multizone modelling of natural and
hybrid ventilation based on state-of-the-art knowledge and to present
topics of current research. The course will be relevant to all PhD
students working in the field of natural and hybrid ventilation. The
course will cover the following topics: Air flow around buildings,
building surface pressures, pressure coefficients, wind and/or thermal
driven flows through single openings, air flow through large openings,
single zone models, multizone models, multiple solutions, dynamical
phenomena, stochastic modelling. The participants will have the
possibility to apply different software packages for various exercises. Duration: 5 ECTS. Numerical and
experimental indoor environmental fluid mechanics The
course will train PhD students in advanced methods and techniques within
measurements and simulation of indoor environmental fluid mechanics. The
course will be relevant to all PhD students working with projects
involving e.g. air distribution in buildings and rooms, comfort and air
quality, cross infection problems, air flow in systems, air flow around
buildings, natural and hybrid ventilation, air flow around persons and
exposure of persons and smoke management in buildings. The course will consist of lectures, study groups and exercises and will
cover topics as: Grid generation, RANS equations and Large Eddy
Simulation, turbulence models for different applications, boundary
conditions for indoor and outdoor air flow, steady state, dynamic and
unstable flow. Quality control of CFD predictions will be a recurring
theme. The participant will have possibility to apply the FLOVENT, FLUENT
and FDS (Fire Dynamics Simulator) software for various exercises. The
course will include a visit to the virtual reality centre (VR Centre) at Duration: 5 ECTS. Experimental Testing for Wave Energy Utilisation and Coastal Engineering Over
the recent years there has been an increased attention to the development
of devices for utilisation of wave energy. This work typically involves at
the earlier stages intensive laboratory model testing in wave tanks and/or
flumes, and at later stages intensive monitoring of prototype testing of
the devices in real seas. At prototype scale the testing typical also
includes testing and improving the control algorithms of the device. The
objective of the course is to introduce and apply wave analysis theory,
laboratory measuring techniques, prototype monitoring and control. The
course will include class room lectures, laboratory exercises in the wave
tanks/flumes and on-site testing at the WEC Wave Dragon prototype in real
sea (Nissum Bredning). The following items will be covered in the course:
Time and frequency domain wave analysis, reflection wave analysis, 3-D
wave analysis, wave groupiness, bound 2nd order waves,
laboratory and prototype measuring techniques for waves, loadings and
power take-off, data management, remote device operation and device
control strategies. The
course is of relevance for PhD students and others with interests in
development of wave energy devices, coastal and offshore engineering. Duration: 2.5 ECTS. Applied
Mathematics The
course introduces some concepts and methods of applied mathematics that
are essential for advanced engineering. The adjoined nature of the
gradient and divergence operator is used to introduce simple elliptic,
parabolic and hyperbolic equations, and to derive and structure the basic
properties of the classical orthogonal polynomials and Bessel functions.
The divergence theorem is used to reformulate the original differential
equation to integral equations or Galerkin (finite element) form. The role of the classical functions as solution to canonical problems
from mechanics and as source solutions for integral equations is
demonstrated. Finally, discretization effects like numerical dispersion
and anisotropy are illustrated. Duration: 5 ECTS Constitutive
Models for Materials The
purpose of this course is to give the theoretical basis for analysis and
design of complex materials such as concrete, soil and composites (e.g.
fibre reinforced concrete). The course will contain formulation of
relevant constitutive models (e.g. based on plasticity and damage theory)
and discuss their numerical implementation. Reference will be given to
available constitutive models in finite element programmes. Duration: 5 ECTS Decision
Theory in Civil Engineering The
purpose of the course is to give the theory for optimal decision making
under certainty. The course will contain elements of basic decision theory,
risk acceptance criteria, reliability methods (stochastic modeling, First
and Second Order Reliability Methods and updating of reliabilities),
Bayesian statistical methods, preposterior analyses, regression models in
Bayesian analysis of experiments and optimal experiment planning under
uncertainty. Further a number of applications in different areas will be
given. Duration: 3 ECTS Advanced
Methods in Stochastic Dynamics of Non-linear Systems The
course will have the following content: Markow and non-Markov excitations.
Modelling assumptions and physical arguments. Dynamic response of
non-linear systems to Gaussian white noise and filtered Gaussian white
noise excitations. Diffusive Markov process techniques. Random pulse
trains driven by different stochastic point processes. Dynamic response of
non-linear systems driven to Poisson impulse excitations. Non-diffusive
Markov process techniques. Non-Markov response problems reducible to
Markov problems. First-passage time problems. Cell-to-cell mapping (path
integration) techniques for the probability density of the response.
Petrov-Galerkin method to solve the forward and backward Kolmogorov
equation. Techniques of equivalent linearization. Stochastic averaging
technique. Duration: 5 ECTS. Numerical and
Experimental Environmental Fluid Mechanics The
objective of the course is to train PhD students in advanced methods and
techniques in environmental fluid mechanics in respect to advection and
mixing of pollutants in turbulent environments. The course will be
relevant to all PhD students working with projects involving turbulent
flow and transport processes in general. Examples of areas with specific
relevance are comfort and ventilation contaminant distribution in rooms,
solids transport and separation in sedimentation and process tanks, as
well as flow in water and marine environments. The course will consist of lectures, study groups and exercises.
Development of transport equations as well as development of one- and two
dimensional Computational Fluid Dynamics will be trained to the
participants. The k epsilon-model will be used in most cases and Large
Eddy Simulation will be discussed. The participants will have the
possibility to use PHOENICS, FLOVENT and CXF Flow3D software in different
exercises. Duration: 5 ECTS Experimental
and Numerical Wave Generation and Analysis The
objective of the course is to train PhD students in advanced methods and
techniques in wave generation in both physical and numerical wave models.
The course will be relevant to all PhD students working with projects
involving gravity water problems. The course will consist of lectures,
study groups and exercises. Theories for a correct modelling of ocean
waves in the laboratory and in numerical models are presented. Important
parameters to describe waves and sea states are reviewed and different
methods of analysing ocean waves are treated. The techniques are
implemented and exercised in the laboratory or in numerical models. Duration: 3 ECTS External
cooperation in connection with the ·
·
COWI ·
Rambøll ·
Vestas ·
Siemens Wind Power ·
·
Danish Technological Institute ·
Norfab (company), Assens ·
ETHZ, ·
Danish Building Research Institute ·
·
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Danish Working Environment Institute. ·
Danish Hydraulic Institute ·
Technical ·
·
·
·
Hydraulics Research, ·
CEPYC, ·
·
·
·
Krüger ·
VBBVIAK, ·
Danish Geotechnical Institute (DGI) ·
Norwegian Geotechnical Institute (NGI), ·
Geological Institute, ·
·
National Survey and Cadastre ·
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Vitus Bering, ·
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VTT
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