master programme „computational engineering“ …€¢ spatial isoparametric truss elements ... -...

RUHR-UNIVERSITÄT BOCHUMFakultät für Bauingenieurwesen

Computational Engineering

Master programme „Computational Engineering“Lectures

Title Page

1st Semester

Compulsory:Mathematical Aspects of Differential Equations and Numerical Methods 4

(Prof. Huckleberry)Mechanics of Solids 5

(Prof. Bruhns)Computer-oriented Design of Steel Structures 6

(Prof. Kindmann)Modern Programming Concepts in Engineering 7

(Prof. Hartmann, Dr. Baitsch)Finite Element Methods in Linear Structural Mechanics 8

(Prof. Meschke, Dr. Kuhl)

Selectable:Tensor Theory in Mechanics and Engineering 9

(Dr. Xiao)

2nd Semester

Compulsory:Fluid Mechanics 10

(Prof. Höffer, Dipl.-Ing. Sahlmen)Continuum Mechanics 11

(Prof. Hackl, Dr. Le)Numerical Methods in Dynamics 12

(Dr.-Ing. Kuhl)

Selectable:Concrete Engineering and Design 15

(Prof. Dr.-Ing. Stangenberg) Theory of Plasticity 16

(Dr. Xiao) Advanced Finite Element Methods 18

(Prof. Dr. techn. Meschke, Dr.-Ing Kuhl) Numerical Methods and Algorithms in Geotechnical Engineering 19

(Prof. Dr. techn. Meschke)Numerical Simulation in Tunnelling 20

(Prof. Dr. tech. Meschke Dipl.-Ing. Carstens) Computational Elasticity and Viscoelasticity 21

(Dr.-Ing. Mosler) Finite Element Technology 22

(Dr.-Ing. Mosler)Computational Modelling of Subsurface Transport Processes 23

(Dr.-Ing. König)

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Environmental Modelling 24(Prof. Dr.-Ing. Stolpe, Dipl.-Ing. Brömme)

Computational Fluid Dynamics 25(Prof. Verfürth)

C++ Tutorial / Programming and Implementation 26(Dr.-Ing. Breidt, Dipl.-Ing. Wellmann)

Object-oriented Modelling and Implementation of Structural Analysis Software 27

(Dr.-Ing. Baitsch, Dr.-Ing. Kuhl)Computational Plasticity 28

(Dr. Hoppe)

3rd Semester

Selectable:

Safety and Reliability of Engineering Structures 29(PD Dr.-Ing. Kasperski)

Design Optimisation 30(Prof. Dr.-Ing. Hartmann)

Parallel Computing 31(PD Dr.-Ing. Leimbach)

Computational Methods in Engineering 32(Dr. Wiebe)

Medical Flow Modelling and Computation 33(Prof. Dr. Rogg)

Soil Dynamics and Soil Structure Interaction 34(not precised jet)

Simulation of Earthquake Loaded Structures 35(Prof. Dr.-Ing. Chouw)

Dynamics of Structures 36(Prof. Dr.-Ing. Höffer)

Fundamentals and Methods of Constructional Product Design 37(not precised jet)

Precision Engineering 38(Dr.-Ing. Witzel)

Adaptive Finite Element Methods 39(not precised jet)

FurtherComputational Modelling of Subsurface Transport Processes 40

(Dr.-Ing. Rosen)Finite Element Technology 41

(Prof. Dr.-Ing. Reese)Numerical Methods in Dynamics 42

(Prof. Dr.-Ing. Reese)Tensor Theory and Computation 43

(Prof. Dr.-Ing. Reese)

Case Studies in Computational Engineering 44(all lecturers related to the Master programme)

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Shortcuts:L = LectureE = ExerciseH = HomeworkS = Seminar

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Mathematical Aspects of Differential Equations and NumericalMethods

Lecturer: Prof. Dr. Dr. h.c. A. T. HuckleberryDepartment: Mathematics II

Complex Analysis

Course content:The course will focus on the mathematical formulation of differential equations withapplications to elastic theory and fluid mechanics.

• Introduction to geometric linear algebra with emphasis on function spaces• Elementary aspects of partial differential equations• The mathematics side of the Finite Element Method for elliptic PDE in low-

dimensionsAppropriate Sobolev geometriesThe FEM for Dirichlet and Neumann problemsError estimatesFast and efficient solvers for the resulting matrix equations

References and reading assignments:will be provided• Claes Johnson, Numerical solutions of partial differential equations by the finite

element method, Cambridge, 1987

Semester:1

ECTS Credits:6

Type of course:2 L/2 E/0 H

Prerequisites:

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Mechanics of Solids

Lecturer: Prof. Dr.-Ing. O.T. BruhnsDepartment: Civil Engineering

Institute of Mechanics

Course content:The objective is to present advanced issues of mechanics and strength of materials.The concepts introduced will be applied to numerous examples in structural mechanics.The following topics will be covered:

• Basic concepts of continuum mechanics • Elastic material • The theory of simple beams I • Torsion of prismatic bars • Curved beams • Simple beams II: Energy principles • Two-dimensional problems • Plates and shells • Stability of equilibrium • Some basic concepts of dynamics • Oscillators with one degree of freedom • Systems of several degrees of freedom • Answers to the exercises

References and reading assignments:• E.A. Fox, Mechanics, Harper & Row, New York, 1967.• F.L. Singer, Strength of Materials, Harper & Row, New York, 1963.

Semester:1

ECTS Credits:6


Prerequisites:

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Computer-oriented Design of Steel Structures

Lecturer: Prof. Dr.-Ing. R. KindmannDepartment: Civil Engineering, Institute of Steel and Composite Structures

Course content:The course includes the design and the construction of steel structures.

• Basic principles of structural design • Verification methods Elastic-Elastic and Elastic-Plastic • Buckling of linear members and frames • Lateral buckling and lateral torsional buckling • Geometric non-linear design of structures - second order analysis • Bolted and welded connections • Composite Beams and Columnes • Design software - RUBSTAHL-programmes • Practical course in the structural Testing Laboratory

References and reading assignments:will be given

Semester:1

ECTS Credits:6


Prerequisites:Fundamental education in mechanics andstrength of materials

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Modern Programming Concepts in Engineering

Lecturer: Prof. Dr.-Ing. D. HartmannDr.-Ing. M. Baitsch

Department: Civil EngineeringInstitute of Computational Engineering

Course content:• Introduction

- Use of computers- Characteristic applications in engineering- What is the problem?- What should be known of computers?- What does “Modern Programming Concepts” mean?- Object-oriented software engineering

• Representation of algorithmic operations- What is an algorithm?- How to describe algorithms

• Details on data structures- General remarks- Arrays- Structures- Linked lists- Stacks, Queues, Trees- Graphs- Object-oriented modelling

• Objects unify data and algorithms- Describing given problems using Object Oriented Analysis- Demonstration of OOA- UML Calculus

• Dynamic modelling- Temporal and time variant aspects- Events- Scenarios, States, Sequence diagrams- Collaboration diagrams- State diagrams

• Functional modelling • Implementation of graphical user interfaces

- Model-View-Controller pattern- Realisation of GUIs with Java

References and reading assignments:will be given during the course

Semester:1

ECTS Credits:6


Prerequisites:

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Finite Element Methods in Linear Structural Mechanics

Lecturer: Prof. Dr. techn. G. MeschkeDr. D. Kuhl

Department: Civil EngineeringInstitute of Structural Analysis

Course content:Finite element discretization techniques for linear elastic static and dynamic structuralanalysis.

• Fundamentals of linear structural mechanics- Continuum kinematics- Continuum kinetics- Initial and boundary conditions- Hyperelastic constitutive laws- Initial boundary value problem of elastomechanics- Weak form of the initial boundary value problem

• Spatial isoparametric truss elements- Fundamental equations of one-dimensional continua- Finite element discretization- Assembly of the structure- Solution of the system equation- Postprocessing

• Plane finite elements- Basic equations of planar continua- Finite element discretization- Bilinear Lagrange element- Rectangular bilinear Lagrange element- Biquadratic serendipity element- Triangular plane finite elements- Numerical integration

• Finite Volume Elements- Fundamental equations of three-dimensional continua- Finite element discretization

References and reading assignments:• Bathe, K. J., Finite Element Procedures, Prentice Hall International Edition,

Englewood Cliffs, 1996. • Hughes, T. J. R., The Finite Element Method. Linear Static and Dynamic Finite

Element Analysis, Prentice Hall International Edition, London, 1987• Zienkiewicz, O. C., Taylor, R. L., The Finite Element Method, Fourth Edition - Volume

1 Basic Formulation and Linear Problems. McGraw-Hill Book Company, London1989.

Semester:1

ECTS Credits:6


Prerequisites:

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Tensor Theory in Mechanics and Engineering

Lecturer: Dr.-Ing. H. XiaoDepartment: Civil Engineering


Course content:• Vectors and vector spaces

- Motivation and examples- Geometric definition and basic operations- Vector spaces- Algebraic expressions in terms of standard bases- Indicial notations and conventions

• Second-order tensors- Motivation and examples: deformation and stress- 2nd-order tensors as linear transformations- Basic operations- Algebraic expressions in terms of standard bases- Characteristic properties- Symmetric, orthogonal and skew-symmetric tensors

• Tensors of higher order- Motivation and examples: piezoelectricity and elasticity- Tensor product- Tensors as linear transformations- Algebraic expressions in terms of standard bases- Contraction as unified product operations- 3rd- and 4th-order tensors- Componentwise expressions

• Scalar, vector and tensor fields- Motivation and definition - Continuity and gradients- Curl, divergence and Laplacian derivatives- Differentiation in Cartesian coordinates- Differentiation in curvilinear coordinates- Integration of scalar and vector fields

• Introduction to tensor functions- Motivation and examples- Material symmetries and constitutive functions- Scalar- and tensor-valued functions- Isotropy and anisotropy- Rivlin-Ericksen theorem

References and reading assignments:

Semester:1

ECTS Credits:4,5


Prerequisites:Linear finite element methods

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Fluid Mechanics

Lecturer: Prof. Dr.-Ing. R. HöfferDipl.-Ing. J. Sahlmen

Department: Civil Engineering, Aerodynamics in Engineering

Course content:The course will focus on the basic principles in fluid mechanics and on its application.

• Introduction to fluid mechanics- Fields of fluid mechanics- History- Practical application: The Boundary Layer Wind Tunnel

• Fluid properties- Density-pressure-compressibility-viscosity

• Fluid statics- Constant density fluid- Variable density

• Kinematics of fluids • Accelerated motion • Transport theorem • Conservation of mass • Conservation of energy • Bernoulli equation • External flows with introduction to the atmospheric boundary layer • Pipe flow

- Without losses- With friction- Laminar and turbulent pipe flow- Losses in pipe flows

• Conservation of linear momentum • Introduction to the Navier-Stokes equation • Computational fluid dynamics

- Theory- Introduction to the programme CFX- Application of CFX


Semester:2

ECTS Credits:6


Prerequisites:Fundamental of mechanics

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Continuum Mechanics

Lecturer: Prof. Dr. rer. nat. K. HacklDr. rer. nat. K.C. Le

Department: Civil EngineeringInstitute of Mechanics

Course content:• Fundamentals

- Vector and tensor analysis- Stresses and equilibrium conditions0- Strains and compatibility

• The field equation of linear continuum mechanics- Hook's law for isotropic materials- Navier and Beltrami-Michell equation

• Displacement functions- Scalar and vector potential- Galerkin vector

• Kinematics- Deformation- Polar decomposition- Analysis of motion

• Balance law- Balance of moment and momentum- Balance of energy- Invariant balance of energy, principle of virtual work- Second law of thermodynamics

• Constitutive equations- Consequence of thermodynamics- Isotropic and homogeneous materials- Examples of constitutive equation

• Boundary value problems- Formulation of boundary value problems- Deformation of a cube under tension- Non-linear wave propagation

References and reading assignments:• T.C. Doyle and J.L. Ericksen, Nonlinear elasticity. In: Advances in Appl. Mech. IV,

Academic Press, New York, 1956• C. Truesdell und W. Noll, The nonlinear field theories. In: Handbuch der Physik

(Flügge Hrsg.), Bd. III/3, Springer-Verlag, berlin, 1965• J.E. Marsden und T.J.R. Hughes, Mathematical foundation of elasticity, Prentice Hall,

1983• R.W. Ogden, Nonlinear elastic deformation, Willy & Sons, 1984

Semester:2

ECTS Credits:6


Prerequisites:

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Numerical Methods in Dynamics

Lecturer: Dr.-Ing D. KuhlDepartment: Civil Engineering, Institute of Structural Analysis

Course content:

Part I - Linear Dynamics

Linear Elastodynamics- Balance of momentum- d'Alembert principle- Hamilton principle- Examples

Finite Element Discretization in Linear Elastodynamics- Generalized multi-dimensional finite element formulation- Consistent load tensor, stiffness tensor and mass tensor- Semidiscrete equation of motion- Physical damping- Implementation and examples

Classification of Numerical Methods for Linear Dynamics

Eigenvalue Analysis- Generalized eigenproblems- Standard eigenproblem- Natural frequencies and eigenforms- Implementation and examples

Finite Difference Integration Schemes- Finite difference scheme- Direct solution- Mass lumping- Decoupled solution- Numerical stability- Implementation and examples

Newmark Integration Schemes- Temporal approximations and algorithmic equation of motion- Family of Newmark schemes (Newmark, Hilber, Bossak, Generalized)- Numerical properties- Error indication and error estimation- Adaptive time stepping- Implementation and examples

Galerkin Time Integration Schemes- Classification- General format of discontinuous and continuous Galerkin schemes- Discontinuous Galerkin schemes- Continuous Galerkin schemes- Single field and two field formulations

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- Error estimation- Adaptive time stepping- Implementation and examplesSpace-Time Finite Elements

• Part II - Non-Linear Dynamics

Non-Linear Elastodynamics- Green-Lagrange strain tensor- Hamilton principle- Linearization- Examples

Finite Element Discretization in Non-Linear Elastodynamics- Generalized multi-dimensional finite element formulation- Internal load tensor and tangent stiffness tensor- Non-linear and linearized semidiscrete equation of motion- Implementation and examples

Finite Difference Integration Schemes- Finite difference scheme- Direct solution- Mass lumping- Decoupled solution- Numerical stability- Implementation and examples

Newmark Integration Schemes- Family of Newmark schemes - Numerical stability- Error indication and error estimation- Adaptive time stepping- Implementation and examples

Energy Conserving/Decaying Schemes- Algorithmic modification of Newmark schemes- Energy conserving/decaying property- Implementation and examples

Galerkin Time Integration Schemes- General format of discontinuous and continuous Galerkin schemes- Discontinuous Galerkin schemes- Continuous Galerkin schemes- Error estimation- Adaptive time stepping- Implementation and examples


• K.-J. Bathe Finite Element Procedures Prentice Hall, 1996

• T. Belytschko and T.J.R. Hughes Computational Methods for Transient Analysis

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North-Holland, 1983 • M.A. Crisfield

Non-Linear Finite Element Analysis of Solids and Structures. Volume 2:Advanced Topics John Wiley & Sons, 1997

• C. Johnson Numerical Solution of Partial Differential Equations by the Finite Element Method Cambridge University Press, 1995

• K. Eriksson, D. Estep, P. Hansbo and C. Johnson Computational Differential Equations Cambridge University Press, 1996

Semester:2

ECTS Credits:6


Prerequisites:Mechanics of Solids

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Concrete Engineering and Design

Lecturer: Prof. Dr.-Ing. F. StangenbergDepartment: Civil Engineering

Reinforced Concrete and Prestressed Concrete Structures

Course content:• Reinforced concrete

- Material behaviour: concrete, steel- Structural design and safety concepts (EC2): safety factors, limit states- Design (EC2): bending, shear, torsion- Exemplary applications to structural systems, redistribution capacities, structuraldetailing

• Prestressed concrete- Loss of prestress: friction, creep, shrinkage, relaxation- Deviation and anchor forces- Computational analysis of prestressed concrete structures

• Non-linear methods for analyses of concrete structures- Yield line theory- Rotation capacity

• Preparation for exam

References and reading assignments:• Eurocode 2: Design of Concrete Structures (ENV 1992).• Concrete Structures, Euro-Design Handbook, Ernst & Sohn Berlin 1994/96.

Semester:2

ECTS Credits:6


Prerequisites:Structural design fundamentals of RCcross sections for bending, longitudinal,transverse and torsional actions

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Theory of Plasticity

Lecturer: Dr. XiaoDepartment: Civil Engineering


Course content:The objective is to present fundamental issues of engineering plasticity as well as someapplications in structural mechanics. This topic is treated as follows:

• 1 Main Features of Elastoplasticity1.1 Pure elasticity1.2 Pure plasticity1.3 Elastoplasticity as combination1.4 The main objectives

• 2 Stress, Strain and Rates2.1 Stressed state and strained state2.2 Stress tensor and strain tensor2.3 Rates (increments) of strain and stress2.4 Eigen expression of stress tensor2.5 Stress space2.6 Vectors, tensors and dot product operations

• 3 Pure Elasticity and Pure Plasticity3.1 Hooke's law for elastic deformations3.2 Flow rule for plastic deformations3.3 Integrations and path dependence

• 4 Yield Limit4.1 Yield limit and its implications4.2 Initial yield limit4.3 Tresca criterion and von Mises criterion4.4 Yield surfaces4.5 Subsequent yield limit with hardening 4.5.1 Isotropic hardening 4.5.2 Kinematic hardening 4.5.3 Combined hardening

• 5 Flow Rules and Evolution Equations5.1 Separation of strain rate5.2 Four cases for deformation behaviour5.3 Elastic rate equation5.4 Flow rule with continuity5.5 Evolution equations for hardening variables5.6 Consistency condition and plastic modulus5.7 Unified loading-unloading conditions5.8 Elastoplastic tensors

• 6 Normality and Convexity6.1 Postulates of plasticity6.2 Standard elastoplatic cycles6.3 Weakened forms of postulates

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6.4 Consequences from Postulate I6.5 Consequences from Postulate II6.6 Essential structure with normality and convexity6.7 J2-flow theories

• 7 Extension and Compression of Bars7.1 Extension and compression of bars7.2 Solutions for perfect elastoplasticity7.3 Solutions for isotropic hardening7.4 Solutions for kinematic hardening7.5 Determination of material parameters


• R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, 1983 • J. Lubliner, Plasticity Theory, Macmillan, New York, 1990 • J. Lamaitre, J.-L. Chaboche, Mechanics of Solid Materials, Cambridge University

Press, 1990 • A.S. Khan, S. Huang, Continuum Theory of Plasticity, John Wiley & Sons, New

York, 1995 • G.A. Maugin, The Thermodynamics of Plasticity and Fracture, Cambridge

University Press, 1992

Semester:2

ECTS Credits:6


Prerequisites:Solid Mechanics, Continuum Mechanics

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Advanced Finite Element Methods

Lecturer: Prof. Dr. techn. G. MeschkeDr.-Ing D. Kuhl

Department: Civil Engineering, Institute of Structural Analysis

Course content:

• Basics of non-linear structural mechanics • Non-linearities of structural mechanics • Material non-linearity • Geometrical non-linearity • Consistent linearization of internal virtual work • Finite element discretization of geometrically non-linear continua • Finite volume elements• Finite truss elements • Solution of non-linear static structural equations • Strategies • Iteration methods • Control of iteration procedures • Stability analysis

References and reading assignments:• Bathe, K. J.

Finite Element ProceduresPrentice Hall International Edition, Englewood Cliffs, 1996.Hughes, T. J. R.The Finite Element Method: Linear Static and Dynamic Finite Element AnalysisPrentice Hall International Edition, London, 1987.Zienkiewicz, O. C., Taylor, R. L.The Finite Element Method: Fourth Edition - Volume 1 - Basic Formulation and LinearProblemsMcGraw-Hill Book Company, London 1989.Crisfield, M. A.Non-linear Finite Element Analysis of Solids and Structures, Volume 1John Wiley & Sons, Chichester 1991.

Semester:2

ECTS Credits:4,5


Prerequisites:Linear finite element methods

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Numerical Methods and Algorithms in Geotechnical Engineering

Lecturer: Prof. Dr. techn. G. MeschkeDepartment: Civil Engineering, Institute of Structural Analysis

Course content:This lecture is concerned with elastoplastic material models including their algorithmicformulation and implementation in the framework of nonlinear Finite Element analyses.In particular, the so-called return map algorithm and the consistently linearized tangentmatrix will be addressed. In addition to models for soils also material models for otherporous and ductile materials will be presented. Applications to nonlinear simulations aswell as typical problems occuring during such analyses will be discussed. Specialattention will be paid to efficient algorithms for nonlinear elastoplastic computations bymeans of the Finite Element Method.


• Simo, JC., Hughes, T.J.R., Computational Inelasticity, Springer, 1997. • D.M. Wood, Soil behavior and critical state soil mechanics, Cambridge University

Press, 1990.

Semester:2

ECTS Credits:3,5


Prerequisites:

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Numerical Simulation in Tunnelling

Lecturer: Prof. Dr. tech. G. MeschkeDipl.-Ing. S. Carstens

Department: Civil Engineering, Institute of Structural Mechanics

Course content:This tutorial provides an overview over the most important aspects of realistic numericalsimulations of tunnel excavation using the Finite Element Method includingconsideration of staged excavation processes and support measures. This includesmaterial modelling, discretization in space and time and the evaluation of numericalresults.In the framework of excercises nonlinear numerical analyses in tunnelling will beperformed by the participants in autonomous teamwork in the computer-lab.


Semester:2

ECTS Credits:1

Type of course:0 L/0 E/0 H/ 1 S

Prerequisites:Participation in the lecture "NumericalSimulation in Tunnelling" is recommended.

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Computational Elasticity and Viscoelasticity

Lecturer: Dr.-Ing. Jörn MoslerDepartment: Lehrstuhl für Technische Mechanik

Course content:

• Finite element method for linearized elasticity theory • Short introduction to nonlinear continuum mechanics • Finite element method for a geometrically exact description • Analogies between the geometrically linearized and the exact finite element

method • Short introduction to constitutive modeling at finite strains • Elasticity theory • Viscoelasticity theory • Integration algorithms


Semester:2

ECTS Credits:3


Prerequisites:

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Finite Element Technology

Lecturer: Dr.-Ing. Jörn MoslerDepartment: Lehrstuhl für Technische Mechanik

Course content:

• Finite element method for linearized elasticity theory• A priori error estimates • Definition of locking effects • Numerical methods avoiding locking

- Reduced integration- Mixed finite element formulations- Enhanced Assumed Strain (EAS) concept

• Generalizations necessary for nonlinear elasticity theory • Mesh generation and refinement strategies


Semester:2

ECTS Credits:3


Prerequisites:

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Computational Modelling of Subsurface Transport Processes

Lecturer: Dr.-Ing. C. KönigDepartment: Delta h

Course content:The course presents the basic physical phenomena, related numerical methods andpractical case studies for groundwater flow and transport processes.

• Physical phenomena in porous and fractured media- Confined and unconfined flow- Variable saturated media- Seepage flow- Advection-dispersion model- Llinear adsorption- Multiphase flow- Density dependent flow- Matrix diffusion in fractured media- Energy transport- Cubic law- Reactive transport- Heterogenety- Non Darcy flow

• Numerical methods- Particle trecking- Random walk- Finite element method- Method of characteristics- Llast square method- Preconditioned conjugate gradient solver- Operator split technique- Upwind methods- Optimisation for inverse modelling- Stochastic generation of fractures

• Applications- Practical projects

References and reading assignments:• Huyakorn, Peter; Pinder, George: Computational Methods in Subsurface Flow;

Academic Press, Inc., San Diego, California, 1983.

Semester:2

ECTS Credits:6


Prerequisites:Mathematics, Fluid Mechanics, NumericalMethod in Engineering; FEM in LinearStructural Mechanics

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Environmental Modelling

Lecturer: Prof. Dr.-Ing. H. StolpeDipl.-Ing. K. Brömme

Department: Civil Engineering

Course content:

The course gives a general introduction to the field of ecological and environmentalmodelling. The main types of models are presented by use of theory, applications,examples. For a deeper understanding there are exercises where the students can useselected small models for training.

• Introduction - Ecology and systems thinking- Environmental modelling

• System dynamics, systems thinking- Concept of system dynamics- Exercises using STELLA and/or POWERSIM

• Surface water modelling- Concepts and examples

• Modelling of remediation by natural attenuation- Basics of flow and transport models, natural attenuation- Exercises using BIOCHLOR and BIOSCREEN

• Dynamic models of aquatic ecosystems- Eutrophication models- Exercises using STEPS lake modelling


Semester:2

ECTS Credits:4,5


Prerequisites:Basics of Mathematics, Physics,Chemistry, Biology

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Computational Fluid Dynamics

Lecturer: Prof. VerfürthDepartment: Mathematics

Numerical Mathematics

Course content:

This course is concerned with the mathematical and numerical aspects of the simulationof incompressible viscous flows. We first derive the basic equation governing viscousflows from the physical conservation laws of mass, momentum and energy. Next webriefly recapitulate the basic facts about finite element methods which are frequentlyused during the course. Then we consider in increasing complexity the stationary linearStokes equations, the stationary incompressible Navier-Stokes equations, and theinstationary. We recapitulate the basic existence, uniqueness, and regularity results,focus on finite element approximations together with a priori error estimates, efficientsolution of the resulting discrete problems by modern iterative techniques, and onadaptivity based on a posteriori error estimates.

References and reading assignments:Will be given during the course.

Semester:2 (probably from SS 2007)

ECTS Credits:6


Prerequisites:-

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C++ Tutorial / Programming and Implementation

Lecturer: Dr.-Ing. BreidtDipl.-Ing. Wellmann

Department: Civil EngineeringInstitute of Computational Engineering

Course content:

The seminar has a focus on a practical introduction to C++-programming. All presentedconcepts will be explained and implemented by means of examples stemming fromstructural engineering.


Semester:2

ECTS Credits:3


Prerequisites:-

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Object-oriented Modelling and Implementation of Structural AnalysisSoftware

Lecturer: Dr.-Ing. M. BaitschDr.-Ing. D. Kuhl

Department: Civil EngineeringInstitute of Computational EngineeringInstitute of Structural Analysis

Course content:

The object of the seminar is to model, implement and verify a finite element programmefor the analysis of spatial truss structures.


Semester:2

ECTS Credits:3


Prerequisites:-

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Computational Plasticity

Lecturer: Dr. Hoppe

Department: Civil Engineering, Institute of Mechanics

Course content:The course provides the theory and algorithmic formulation for elastoplastic materialmodels considering large inelastic deformation.

• Review of continuum mechanics • Infinitesimal theory of plasticity • Finite strain plasticity theory • Algorithmic structure of finite strain plasticity • Return map algorithm for geometrically linear elastoplastic models • Implemantation of the algorithm in finite element codes • Summary of the algorithm • Selected applications (geomechanical problems)

References and reading assignments:• Simo, J.C., Hughes, T.J.R., Computational Inelasticity, Springer, 1997.

Semester:2

ECTS Credits:3


Prerequisites:Mathematics

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Safety and Reliability of Engineering Structures

Lecturer: PD Dr.-Ing. M. KasperskiDepartment: Civil Engineering

Institute of Structural Analysis

Course content:• Introduction - causes of failures• Basics definitions - safety, reliability, probability, risk• Basic demands for the design and appropriate target reliability values

Structural safetyServiceabilityDurabilityRobustness

• Formulation of the basic design problem: R>E• Descriptive statistics

Position: mean value, median valueDispersion: range, standard deviation, variation coefficientShape: skewness, peakedness

• Theoretical distributions• Discrete distributions: Bernoulli and Poisson Distribution• Continous distributions: Rectangular, Triangular, Beta, Normal, Log-Normal,

Exponential, Extreme Values• Failure probability and basic design concepts• Code concept - level 1 approach• First Order Reliability Method (FORM) - level 2 approach• Full reliability analysis - level 3 approach• Probabilistic models for actions: dead load, imposed loads, snow and wind loads,

combination of loads• Probabilistic models for resistance: cross section - structure• Further basic variables: geometry, model uncertainties• Non-linear methods and Monte-Carlo Simulation


Semester:3

ECTS Credits:6


Prerequisites:Basics of Statistics

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Design Optimisation

Lecturer: Prof. Dr.-Ing. D. HartmannDepartment: Civil Engineering

Institute of Computational Engineering

Course content:• Introduction

Definition of optimisation problemsHistory of optimisation

• Design as a processConventional designOptimisation as a design tool

• Optimisation from a mathematical viewpointNumerical approachesLinear optimisationConvex domains, partioned domainsExamples

• Categories of opt. variablesExplicit design variablesSynthesis and analysisDiscrete and continuous variablesShape variables

• Dependant design variables• Realisation of constraints

Explicit and implicit constraintsConstraint transformationEquality constraints

• Optimisation criterionObjectives in structural engineering

• Application of design optimisation in structural engineeringTrusses and beamsFramed structuresPlates and shellsMixed structures

• Solution techniquesDirect and indirect methodsGradientsHessian matrixKuhn-Trucker conditions

• Project work in structural optimisation


Semester:3

ECTS Credits:6


Prerequisites:

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Parallel Computing

Lecturer: PD Dr.-Ing. K.-R. LeimbachDepartment: Civil Engineering

Institute of Computational Engineering

Course content:The course will cover the basic concepts of parallel computing, the softwaredevelopment and programing methodologies for different parallel machines, and thedesign of parallel algorithms for compute-intensive methods in structural analysis anddesign, outlined as fallows

• Basic Concepts of Parallel Computing - Parallel computer architectures- Operating systems- Programing languages- Programing models for shared and distributed memory parallel machines andparallel virtual machines

• Computational Methods and their Parallel Formulations Direct and alternative methods for the solution of systems of linear equations- Domain composition methods- Substructure methods in static analysis- Method of sensivity analysis in the static reanalysis and structural optimization- Solution of eigenproblems- Transient dynamic analysis- Nonlinear structural analysis

• Computational Implementation and Parallel Applications - Use of a multiprocessor compute server- Transputer cluster and workstation cluster- Programing in a standard language, a concurrent language and a symboliclanguage- Building parallel applications for various structural analysis and design problems


Semester:3

ECTS Credits:4,5


Prerequisites:

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Computational Methods in Engineering

Lecturer: Dr. Wiebe

Department: Mathematik IXAlgebra/Mathematik

Course content:


Semester:3

ECTS Credits:3


Prerequisites:

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Medical Flow Modelling and Computation

Lecturer: Prof. Dr. B. RoggDepartment: Mechanical Engineering

Thermo- and Fluiddynamic

Course content:• Introduction to medical flows• The equations governing medical flows• Properties of blood and blood vessels• Tissue behaviour and fluid/tissue interaction• The Finite Volume Method for medical flows• Computational urological flows• Computational arterial flows


Semester:3

ECTS Credits:4.5


Prerequisites:

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Soil Dynamics and Soil Structure Interaction

Lecturer: not precised jet

Department:

Course content (till WS05/06):The course gives the basic properties and assumptions for the soil related to dynamicanalysis and gives a unified approach for the simulation of the dynamic behaviour of thelinear coupled soil-structure system:

• Introduction to soil dynamics - Dynamic behaviour of soils- Material properties and their measurements- Soil liquification

• Propagation of waves in soil - Navier´s wave equation- Body waves and surface waves- Refraction and reflection of waves in layered soils

• Vibration of foundations - Simplified method- Impedance and compliance- Rigid and elastic foundations- Surface foundations- Deep foundation

• Introduction to interaction problems - Sub-domain method- Free field- Kinematic interaction- Inertial interaction- Wave propagation- Assessment of vibration level- Reduction of vibration

• Numerical methods to solve interaction problems - Finite element method- Boundary element method- Thin layer method

• Case studies with the computer

References and reading assignments:• Richert; F.F; Woods,R.D.; Hall, J.R.: Vibration of soils and foundation; Prentice Hall,

1970.

Semester:3

ECTS Credits:4,5


Prerequisites:Finite Element Methods in LinearStructural Mechanics, Dynamics ofStructures

34/44



Simulation of Earthquake Loaded Structures

Lecturer: Prof. Dr.-Ing. N. ChouwDepartment: Disaster Prevention Engineering II

Okayama University

Course content:The course describes the controlling factors for the earthquake response of structuresand the earthquake resistance design.

• Earthquake engineering- Cause of earthquakes- Seismological and engineering characterisations- Characteristics of near and far source earthquakes- Damage potential

• Earthquake design procedures- Philosophy of earthquake-resistant design- Structural ductility- Elastic and inelastic earthquake design spectra- Design codes- Equivalent static analysis- Time-history procedure- Response spectrum concept

• Relationship between earthquake eycitations and structural responses • Effect of near-source earthquakes on structures • Dynamic properties of soil-structure systems

- Simplified model- Effect of soil-structure interaction on structural responses

• Control of earthquake-induced vibrations- Reduction approaches- Dynamics of base-isolated structures - Governing factors- Analysis procedure

• Cases studies

References and reading assignments:• Script

Semester:3

ECTS Credits:4,5


Prerequisites:Fundamental of Mechanics

35/44



Dynamics of Structures

Lecturer: Prof. Dr.-Ing. R. HöfferDepartment: Civil Engineering

Aerodynamik im Bauwesen

Course content:• Introduction• Linear differential equations of motion• Response of linear oscillators to dynamic loads

Eigenfrequency, damping mechanisms and complex representationImpedance and phase

• Integration procedures in the time domainImpuls response function and Duhamel-integralStep-response function

• Multi-degree of freedom systems and modal analysisComputer-orientated representation of the equation of motionDecoupling by transformation using modal coordinatesIterative procedures for the computation of eigenvectorsModale superposition

• Calculation in the frequency domainFourier-transformation of stationary processesCorrelation and spectrum

• Stochastic oscillationsStatistical parameters, ergodicity and stationaritySpectral and cross-spectral density functions of broad-banded processesApplication to engineering structures Superposition of statistical processes

• The Monte-Carlo method Generation of autoregressive time seriesTime domain calculations

• Equivalent statistical linearization• Applications

Seismic excitation and response spectrumExcitation from wind and waves and spectral method


Semester:3

ECTS Credits:6


Prerequisites:

36/44



Fundamentals and Methods of Constructional Product Design

Lecturer: not precised jetDepartment:

Course content (till WS06/06):• Methodical steps and tools in the developing phases:

Planning, Conception, Designing, Detailing - Controlling• Subjects:

Target costing, Value Analysis, FMEA (Failure Mode Effect Analysis), ...


Semester:3

ECTS Credits:4.5


Prerequisites:

37/44



Precision Engineering

Lecturer: Dr.-Ing. U. WitzelDepartment: Mechanical Engineering

Maschinenelemente und Konstruktionslehre

Course content:• Precision mechanics• Materials of the precision engineering• Composite structures• Manufacturing methods with laser light, electron beams, ultrasonic and pressure

water• Precision engineering springs and bearings and further precision engineering

machine elements• Organization and interpretation of fine machines

• Meaning and advancement of fine mechanics to the micro mechanicsFine mechanics developed in the construction technology to a significant field ofactivity with small applicant number and vocational possibilities. Fine componentsand their fabrication for the automated manufacturing are based on precisionelements and concomitantly on special arts of manufacturing. In and output devicesof the data processing form advanced products of precision engineering. Its advanceprogress in the micro mechanics; see lecture offer of the LMK in the SS and WS.Micromechanical elements can coupled outstanding with microelectronic circuits. Themonolithic integration plays a special meaning, since it permits the furtherdevelopment step to the nano-technology.


Semester:3

ECTS Credits:3


Prerequisites:

38/44



Adaptive Finite Element Methods

Lecturer: not precised jetDepartment:

Course content (till WS05/06):• Introduction• Notation• Basic a posteriori error estimates• A catalogue of error estimators• Mesh adaptation• Data structures• Stationary iterative solvers• Multigrid methods


Semester:3

ECTS Credits:6


Prerequisites:

39/44



Computational Modelling of Subsurface Transport Processes

Lecturer: Dr.-Ing. B. RosenDepartment: Aquium

Course content:The course presents the basic physical phenomena, related numerical methods andpractical case studies for groundwater flow and transport processes.

• Physical phenomena in porous and fractured media- Confined and unconfined flow- Variable saturated media- Seepage flow- Advection-dispersion model- Llinear adsorption- Multiphase flow- Density dependent flow- Matrix diffusion in fractured media- Energy transport- Cubic law- Reactive transport- Heterogenety- Non Darcy flow

• Numerical methods- Particle trecking- Random walk- Finite element method- Method of characteristics- Llast square method- Preconditioned conjugate gradient solver- Operator split technique- Upwind methods- Optimisation for inverse modelling- Stochastic generation of fractures

• Applications- Practical projects

References and reading assignments:Huyakorn, Peter and Pinder, George, Computational Methods in Subsurface

Flow, Academic Press, Inc., San Diego, California, 1983.

Semester:2

ECTS Credits:4,5


Prerequisites:Mathematics, Fluid Mechanics, NumericalMethod in Engineering, FEM in LinearStructural Mechanics

40/44



Finite Element Technology

Lecturer: Prof. Dr.-Ing. S. ReeseDepartment: Civil Engineering, Computational Mechanics and Simulation

Course content:

• Motivation • Alternative representation of the linear standard displacement formulation • Locking • Mixed methods

- B-Bar- Enhanced strain method

• Reduced integration • Large deformation concepts • Structural mechanics

- Beam - Shell

References and reading assignments:Script Finite Element Technology Part 1

Semester:2

ECTS Credits:4,5


Prerequisites:

41/44



Numerical Methods in Dynamics


Course content:Introduction into discretization methods, discrete oscillators, equation of motion, statespace representation, numerical solution techniques, linear equation systems, numericalsignal analysis, subspace method, numerical simulation with MATLAB and SIMULINK,applications: beam and plate structures.

• Single degree-of-freedom systems • Multi degree-of-freedom-systems • Algorithms to integrate second order differential equations

- Finite differences- Newmark method- Stability analysis- Generalized alpha-method

• Deterministic signals and processes- Periodic signals (Fourier series)- Non-periodic signals (continuous and discrete Fourier transformation)

• Excursion to stochastic system identification • Eigenvalue problems

- Basic properties- Algorithmic treatment (vector iteration, subspace iteration, QR algorithm)


• A. K. Chopra, Structural Dynamics, 1995 • R. W. Clough & J. Penzien, Dynamics of Structures, 1993 • Clark, Saunders & Gibbs, Adaptative Structures: Dynamics and control, 1996

Semester:2

ECTS Credits:6


Prerequisites:Mechanics of Solids

42/44



Tensor Theory and Computation


Course content:• Motivation • Introduction into Fortran and C • Vector algebra • Tensor algebra • Computations (tensor algebra) • Tensor product • Spectral decomposition, Cayley-Hamilton theorem • Symmetric and skew-symmetric tensors • Orthogonal tensors • Polar decomposition • Computations (tensor rules) • Coordinate representations • Scalar, vector and tensor fields • Integral theorems • Computations (tensor analysis)

References and reading assignments:References will be given during the lecture.

Semester:1

ECTS Credits:3


Prerequisites:

43/44



Case Studies in Computational Engineering

Lecturer: all lecturersDepartment:

Course content:• Two case studies can be made during the study, each with 3 Credits• The case studies should be related to a lecture from the previous study


Semester:1/2/3

ECTS Credits:3


Prerequisites:

44/44

master programme „computational engineering“ …€¢ spatial isoparametric truss elements ... -...

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