Andreas Zilian joined the University of Luxembourg in 2011 as Professor in Engineering Sciences with focus on Mechanics and Structural Analysis. Based on rich experience as Assistant Professor of Fluid-Structure Interaction and Director of the interdisciplinary and inter-faculty Master Programme on Computational Sciences in Engineering at Technische Universität Braunschweig, he built up the engineering research area of Structural Analysis and Multiphysics Modelling and Simulation within the Department of Engineering at the Faculty of Science, Technology and Medicine. Since 2012 he promotes Computational Sciences as an interdisciplinary theme at the University of Luxembourg, outreaching to national public research institutions and industrial partners. Complementing research and graduate/doctoral teaching activities in Computational Mechanics, he organised several conferences, workshops and mini-symposia. Principal investigator in several third-party funded projects at the national, European and international scale. Regular evaluator for national research funding and teaching programme accreditation agencies, reviewer for several leading scientific journals.

Professional Bio

• Visiting Professor, Technische Universität Graz (06/2016 – 07/2016)
• Full Professor, University of Luxembourg (08/2011 – present)
• Assistant Professor (W1), Technische Universität Braunschweig (03/2006 – 08/2011)
• Visiting Postdoctoral Researcher, Conservatoire National des Art et Métiers Paris (Fall 2005)
• Postdoctoral Researcher, Technische Universität Braunschweig (05/2005 – 02/2006)
• Doctoral Researcher, Institute of Structural Analysis, TU Braunschweig (10/2001 – 09/2004)

Responsibilities

• Coordinator, Doctoral Training Unit DRIVEN (09/2018 – present)
• Head, Institute of Computational Engineering and Sciences at FSTM/UL (06/2016 – present)
• Head, Doctoral School Programme Civil Engineering Sciences (06/2016 – 08/2018)
• Associated Member, Institute of Civil and Environmental Engineering (06/2016 – present)
• Elected Member, Faculty council, FSTM, University of Luxembourg (09/2013 – 09/2018)
• Dean of Studies, MSc CSE, TU Braunschweig (10/2009 – 08/2011)
• Executive Director, Computational Sciences in Engineering, TU Braunschweig (10/2004 – 08/2011)

Education

• Habilitation equivalent, Technische Universität Braunschweig (03/2009)
• Doktor-Ingenieur, Technische Universität Braunschweig (05/2005)
• Diplomingenieur in Civil Engineering, Technische Universität Berlin (09/2001)

Scientific Awards & Honours

• Marie Curie Career Integration Grant, European Commission (2012)
• Exchange Grant, German Academic Exchange Service DAAD (2010)
• Invited Research Fellowship Grant, Bourse de la Ville de Paris (2009)
• PhD Fellowship, GRK432, Deutsche Forschungsgemeinschaft DFG (2001 – 2004)

Affiliations

• International Association for Computational Mechanics (IACM)
• German Association for Computational Mechanics (GACM)
• Gesellschaft für Angewandte Mathematik und Mechanik (GAMM)
• Association Calcul des Structures et Modélisation (CSMA)
• Forschungsvereinigung Baustatik-Baupraxis

Journal Reviews

• Acta Mechanica
• Archive of Applied Mechanics
• Finite Elements in Analysis and Design
• Computer Methods in Applied Mechanics and Engineering
• Computers & Mathematics with Applications
• Applied Energy
• Engineering Computations
• IEEE Access
• IEEE/ASME Transactions on Mechatronics
• Smart Materials and Structures
• International Journal for Numerical Methods in Engineering
• International Journal of Impact Engineering
• International Journal of Mechanical Sciences
• Journal of Micromechanics and Microengineering
• Soil Dynamics and Earthquake Engineering
• Journal of Fluids and Structures
• International Journal for Numerical Methods in Fluids
• Communications in Numerical Methods in Engineering

Selected Academic & Professional Services

• Organiser, Exploratory Workshops on Model Order Reduction (2015, 2017)
• Workgroup Leader, COST Action EU-MORNET (2013 – 2018)
• Member, Editorial Board, Acta Mechanica, Springer (since 2014)
• Initiator, Luxembourg Summer School in Computational Engineering Sciences (2013)
• Guest Editor, International Journal for Numerical Methods in Engineering, Wiley, Special Issue XFEM: Extended Finite Element Methods (2011)
• Conference Chairman, Initiator and Organiser, ECCOMAS Thematic Conference: Extended Finite Element Methods - XFEM, RWTH Aachen University (2009)
• Auditor, Teaching Programme Accreditation, ASIIN (since 2009)

Funding

• European Commission (FP7, H2020)
• Fonds National de la Recherche (FNR)
• Deutsche Forschungsgemeinschaft (DFG)
• Deutscher Akademischer Austauschdienst (DAAD)
• Alexander-von-Humboldt Foundation (AvH)
• Luxembourg Ministère de l’Économie

Last updated on: 11 Apr 2020

Postdoctoral Researchers

• Dr. Christophe Hoareau: Solid and fluid dynamics, vibrations, aero/hydro-elasticity, piezoelectricity (since 09/2019)
• Dr. Hamidreza Dehghani: Poroelasticity, homogenisation, artificial neural networks, machine learning (since 08/2019)

Doctoral Researchers

• Diego Kozlowski: Science of science: Large-scale data mining and analysis of scientific networks and innovation in research, DTU DRIVEN funded PhD project, cross-disciplinary with social sciences and computer science (01/2020–now, ongoing)
• Chrysovalantou Kalaitzidou: Data-integrated multiscale modelling of fibrous extracellular matrix materials, structurally funded PhD project (11/2019–, ongoing)
• Vu Chau: Constitutive characterisation of heterogeneous materials using (deep) artificial neural networks, DTU DRIVEN funded PhD project (07/2019–, ongoing)
• Lan Shang: Data-driven reduced-order modelling of coupled aeroelastic-electromechanical systems, structurally funded PhD project (05/2019–, ongoing)
• Michal Habera: Predictive modelling and simulation of 3D concrete degradation, EU-FEDER funded PhD project, collaboration with Empa/ETH Zürich (11/2017–, ongoing)
• Marco Magliulo: Non-localized contact between beams with circular and elliptical cross-sections, UL funded, (jointly with Dr. L. Beex, 04/2016–03/2020)

Alumni and Former Members

• Dr. Davide Baroli: Reduced basis methods for incompressible fluids and fluid-structure interaction, PostDoc (2017–2019)
• Dr. Haiqin Huang: Predictive modelling of the rheological behaviour of fresh self-compacting concrete, PhD (2015–2019), PostDoc (2019)
• Dr. Srivathsan Ravi: Numerical modelling of piezoelectric energy harvesting devices driven by flow-induced vibrations, PhD (2013–2017), PostDoc (2018)
• Dr. Amalya Khurshudyan: Comparative study of reduced-order methods for geometrically nonlinear structures, PhD (2012–2017)

Last updated on: 11 Apr 2020

Research Concept

Current research aims at addressing application-driven problems related to statics and dynamics of structures and continua, aspects of computational mechanics as well as the development and validation of advanced models and methods in computational engineering and simulation. While the character of the research work has its roots in the engineering sciences, research lines have become increasingly interdisciplinary and stretch to a wide range of disciplines in science, e.g. physics, computer science, applied mathematics but also the life and social sciences.

All interdisciplinary research activities aim at the simultaneous investigation of

• the involved physical phenomena,
• the identification of appropriate mathematical models and their validation,
• the development and application of efficient approximate solution methods, and
• the transformation of research findings to practically applicable formats (norms, guidelines).

Within the space spanned by the above guiding aspects, particular thematic expertise has been developed in the following areas.

Hypothesis-driven modelling of multi-physics problems

• self-excitation phenomena in aeroelasticity and hydroelasticity
• wind engineering and related reduced coupled engineering models
• optimisation and optimal control of structures in fluid flow
• piezoelectric materials and composites for energy harvesting
• contact of slender structures

Hypothesis- and data-driven modelling of materials

• hydration processes and rheological characterisation of setting fresh concrete mixtures
• ageing of concrete structures and integration into BIM-serviced material banks
• granular materials with phase transitions
• data-informed homogenisation and multiscale modelling of porous materials
• characterisation of fibrous materials and biological tissue (extracellular matrix)

Computational mechanics

• advanced finite element methods
• generalised approximation methods based on weighted residuals
• coupling strategies for strongly-coupled multiphysics systems
• numerical approaches for interfaces and moving boundaries
• methods for reduced order modelling of nonlinear parameterised problems
• data-driven model generation using machine learning approaches
• automated code generation for integration of hypothesis-driven and data-driven models

Research Portfolio

An overview of the current research lines is given below.

Doctoral Research

Non-localised contact between beams with circular and elliptical cross-sections

Numerous materials and structures are aggregates of slender bodies, e.g. struts in metal foams, yarns in textiles, fibres in muscles or steel wires in wire ropes. To predict the mechanical performance of these materials and structures, it is important to understand how the mechanical load is distributed between the different bodies. If one can predict which slender body is the most likely to fail, changes in the design could be made to enhance its performance. As the aggregates of slender bodies are highly complex, simulations are required to numerically compute their mechanical behaviour. The most widely employed computational framework is the finite element method in which each slender body is modelled as a series of beam elements. On top of a mechanical representation of the individual slender bodies, the contact between the slender bodies must be accurately modelled. While contact between beam elements has received wide-spread attention, the focus was mainly directed towards beams with circular cross-sections, whereas elliptical cross-sections are also relevant for numerous applications. In this project, different frameworks for beams with elliptical cross-sections are proposed in case a point-wise contact treatment is insufficient. This includes a framework for contact scenarios where a beam is embedded inside another beam, which is in contrast to conventional contact frameworks for beams in which penetrating beams are actively repelled from each other. The novel contact frameworks are enhanced with frictional sliding, where friction not only occurs due to sliding in the beams’ longitudinal directions but also in the transversal directions. [Marco Magliulo]

Rheological behaviour of fresh self-compacting concrete

Fresh concrete mixtures essentially contain water, cement and rigid aggregates of a characteristic size distribution, which are embedded in the liquid-like cementitious matrix. The specific choice of ingredients and their volume fractions defining the immediate rheological properties of the mixture, primarily the yield stress and apparent viscosity, have great influence on the processability of the concrete mixture during on-site operation. Right after mixture, fresh concrete preserves its characteristic viscosity for a limited amount of time (the dormant stage, lasting for less than 60 minutes). As chemical reactions start to set in (hydration), the microstructure of the cementitious phase changes by developing growing fibrous structures (within hours), that – over time – increasingly modify the macroscale properties of the material and finally constitute the hardened porous skeleton (within days). The interaction of mechanical, chemical, hygral and thermal processes during the in-between stage (the setting stage) is in principle well understood with respect to observable microphysical processes, however, predictive models for the complete fresh stage of concrete are not yet available. This contribution focuses on the consistent mathematical modelling of the hydration-driven phase-transformation from fluid-like to solid-like behaviour of the SCC concrete mixture. The model includes: (1) a phase-field approach for (thermo-dynamically) consistent description of the cement paste as a single-component flow and its phase change from fluid to solid, (2), a continuum model with elasto-visco-plastic constitutive behaviour based on the local phase-field quantity, and (3) a multi-component or mixture model that allows description of the fresh concrete as a suspension consisting of the (phase-changing) cement paste and aggregates. The nonlinear model is brought to integral form using the method of weighted residuals and discretised with finite elements using on the open-source finite element framework FEniCS. [Haiqin Huang]

Predictive modelling and integrated simulation of 3D concrete degradation

Long-term behaviour of concrete structural elements is very important for evaluation of its health and serviceability range. The phenomena that must be considered are complex and lead to coupled multiphysics formulations. Such formulations are difficult not only from physical perspective, but also from computational perspective. The projects makes a contribution to implementation and optimisation of state-of-the art concrete ageing models with the finite element method, specifically using the open-source package FEniCS. The physical model represents an ageing linear viscoelastic material with damage, based on the works of Z. Bazant and J. Mazars. The goal of this research is a high-performance code for long-term concrete behaviour that can be used for simulation of real, large-scale structures in reasonable times on low to mid-range computing facilities. Part of the research is an active contribution to the development of the FEniCS finite element package, including domain specific languages, code generation, compiler optimisation techniques and general software engineering tasks with focus on performance, parallelism (instruction level or MPI) and scalability. [Michal Habera]

Data-driven computational continuum mechanics

This project focuses on developing and investigating computational data-driven methods in order to model the material laws from observed data. The methodology is expected to deliver the governing mathematical model of the observed problem in the form of a set of symbolic equations which potentially enable new discoveries in data-rich fields of continuous physical problems. Artificial neural networks (ANN) have been proposed as an efficient data-driven method for constitutive modelling, accepting either synthetic data solutions or experimental datasets. Sparse regression has the potential to identify relationships between field quantities directly from data in form of symbolic expressions. Depending on the richness of the given data (function values vs. gradients, densely vs. sparsely sampled) specific techniques are required to obtain accurate numerical evaluations of spatial and temporal derivatives from sparse data representing smooth or non-smooth states; e.g. via hierarchical multi-level gradient estimation, Gaussian smoothing or gradient capturing techniques. A machine learning prototype is implemented using the FEniCS framework coupled to a trained neural network on the basis of PyTorch. [Vu Chau]

Computational reduced order modelling of energy harvesting devices driven by flow-induced vibrations

Piezoelectric energy harvesters (PEHs) are a potential alternative to batteries in large-scale sensor networks and implanted health trackers, but the low output power and the narrow operation range has been a bottleneck for their practical application. To alleviate this problem, this project develops a data-driven reduced-order model for flow-driven PEHs based on the dataset obtained from a nonlinear and parametrised electro-mechanical model. The high-fidelity monolithic computational model of the fluid-structure-piezo-circuit coupled problem is established on basis of the weighted residuals method and corresponding numerical solutions will be obtained using a finite element method discretisation (FEniCS). A projection-based model order reduction will be implemented and machine learning will be introduced to identify a suitable reduced basis representation in the presence of nonlinearities and many parameters. The validated reduced-order model is expected to provide a reliable and fast way to predict and optimise performance of flow-induced PEHs, thereby promoting further commercialisation of such devices. [Lan Shang]

Data-integrated multiscale modelling of fibrous extracellular matrix materials

One of the key questions in cellular biology concerns the detailed understanding of how a particular cell orchestrates its behaviour with that of neighbouring cells within a tissue. Not only the intrinsic genetic programme of the cell, but also external influences, such as those exerted by its microenvironment, drive these important functions. Key component of this microenvironment is the Extracellular Matrix (ECM), a convoluted network of fibrous proteins, which interacts directly with cells and provides the means of cellular communication through biomechanical signals. Cells sense and respond to mechanical action by inducing deformation fields that propagate over a long range, sufficient to reach other cells and enable their interaction. The effects of these interactions include differentiation tendency of stem cells, as well as cell migration and regeneration. Understanding the mechanism underlying the propagation of the deformations that drive these phenomena is equivalent to characterising the mechanical properties of ECM. Being a network of biopolymers (fibres), the mechanical state of ECM is attributed to the mechanical properties of its individual fibres. Although there exist several computational models trying to simulate their behaviour, they entirely depend on the constitutive mathematical model that each of these introduce. Here we propose a novel study that integrates classical mechanical modelling at micro/fibre scale with data-driven methods at the meso/macro-scale, in order to deliver a comprehensive analysis of the ECM deformation-related phenomena along with parameter exploration. This interdisciplinary approach aims at exploiting the reinforcement learning paradigm with experimental and simulated data to identify and quantify the ECM-material model properties that allow the characterisation of deformations that drive cellular function and intercellular communication. The completion of this project will lead the way for constitutive-free, data-driven modelling of ECM and an improved understanding of what perturbations in its parameter and model space may control cellular behaviour. [Chrysovalantou Kalaitzidou]

The networks of science: data-driven understanding of scientific production

The quantitative study of science is a developing research stream. The systematisation of research communications, in particular research articles, open the possibility to data-driven approaches to shed new light into old questions regarding the way in which our society increase its knowledge. This implies the opportunity to go from the traditional meta-scientific epistemology to new scientific approaches of research. The quantifiable product of science has shown an exponential growth since the standardisation of research papers as the way of communicating results. Besides, the advances on communication technologies simplify the exchange between researchers in distant places, and the international collaboration experienced an exponential increase. All these refers to a network in permanent expansion and densification, that increasingly demands computational-based methods to study it. At the same time that research becomes a complex system, new tools from statistics and computer sciences are developed in order to handle this type of information. Natural Language Processing give the opportunity to harness textual information, while Graph Theory helps to understand complex networks that cannot be studied shallowly. The main objective of the project is to advance in the understanding of Science’s development across fields and countries, in our current society, from a data-driven perspective, both from a epistemic (how knowledge is generated an spread) and social (science production as a part of society) perspective. [Diego Kozlowski]

Postdoctoral Research

Reduced order models and methods for coupled nonlinear multi-physics problems

Flutter-induced piezoelectric energy harvesters (PEHs) allow the provision of an autonomous source of low-power energy to small electronic devices (e.g. structural health-monitoring sensors) operated in remote locations. The design of PEHs has to take into account a wide range of operational conditions (flow velocities), requiring consideration of large-amplitude structural vibrations to maximise the power output while minimising exposure to fatigue. The coupled aeroelastic/piezoelectric/circuit problem poses multiple challenges: (1) modelling and predicting the nonlinear dynamic behaviour of a fluid-structure-piezoelectric system, (2) quantify the power output sensitivity under changing conditions (e.g. varying flow input velocity) with flutter instabilities, (3) allow just-in-time feedback to control and propose optimal designs of parameterised PEHs. The provision of a multi-parametric virtual abaqus using off-line (numerical) solutions to high-fidelity computational models in order to reconstruct on-line approximations is crucial to overcome those three challenges. Data-driven Reduced Order Models (ROM) and associated methods are investigated. Numerical solutions calculated with the open-source software FEniCS and experimental quantities of interest are generated to establish a high-fidelity off-line data-base. Machine learning algorithms are used to explore the data on the system behaviour (snapshots) for basis generation of the highly nonlinear system. [Christophe Hoareau]

Mechanical modelling of poroelastic media using data-driven approaches

Poroelastic materials are applicable in numerous disciplines ranging from soil and concrete in engineering to brain and tumour tissues in biology. Predictive analysis of this type of media requires complex multiscale and multiphysics modelling due to the sharp difference in length scale of the average pore (microscale) and the specimen (macroscale) as well as the fluid flow through the pore space. Micro- and macroscale response (fluid and solid response) are strongly coupled. The multiscale physical modelling is challenged by the homogenisation step and the localisation phenomenon, which can be approached via a combination of analytical and direct numerical approaches. However, this is often either not efficient or requires further simplification to allow treatment of real-world industrial problems. Data-driven approaches such as Artificial Neural Networks (ANNs) are promising tools to replace the whole or certain parts (e.g. constitutive relationships or time integration) of Direct Numerical Solution (DNS) for such complex problems. In this investigation of data-driven approaches for poroelastic problems the focus is on (1) identify homogenised poroelastic model parameters, (2) obtain continuous solution of the macroscale system of PDEs, (3) perform material remodelling due to macroscale response (localisation and homogenisation), (4) include the effect of macroscale response in the appositional growth of the tissue (localisation and homogenisation), (5) microscale properties identification from the snapshots of experimental tests (image recognition, material parameter identification, and localisation). [Hamidreza Dehghani]

Last updated on: 11 Apr 2020

Teaching Concept

Thematic learning, the development of technical skills as well as the acquisition of confidence in the various subjects related to Mechanics and Structural Analysis is often a serious challenge for engineering students, in particular during their undergraduate studies. While there are likely many different reasons for this phenomenon, teaching experience and student feedback shows that a key aspect for successful learning is the sensation of creativity. Teaching of mechanics – statics, dynamics, materials – therefore should put the learner in an active role: someone who makes very conscious decisions about observations of physical reality, associated abstractions and simplifying assumptions, someone with a critical eye on the implications of such modelling decisions, but also someone who learns to reliably and responsibly take advantage of the potential presented by predictive models in engineering.

Since training of future engineers must aim at providing a profound basis for a large part of an engineering career, a key mission for teaching of Statics and Dynamics of Structures is to develop the student’s ability to model, analyse, control and optimise as well as to assure quality of engineering structures and cross-disciplinary engineering systems in general. This is in particular true for the ongoing digital transformation that affects all engineering disciplines. Highly-detailed and sophisticated digital twins of engineering projects will become standard during the professional life of today’s students.

Through a combination of course work, case studies, individual and team projects the students are educated in a wide range of relevant theoretical and practical aspects of Structural Analysis. New topics and aspects are introduced in a curiosity-driven or application-driven approach. Proper understanding and consistent application of the underlying and recurring basic mechanical principles and mathematical techniques is a core objective of all teaching activities. This is complemented with the discussion or demonstration of practical examples.

For all courses the basic course information, work load calculation, thematic references, course evaluation procedures, examination modalities and well as a weekly breakdown of lecture/exercise content together with all teaching and learning material is available online (Moodle).

Teaching Portfolio

An overview of the overall teaching portfolio at the undergraduate and graduate level is given below. This involves courses taught in the past and current teaching/training activities (marked with *).

The language of course instruction (lectures, exercises, tutorials, consultation) is chosen on basis of the student’s preference, typically English, German or French.

Bachelor Courses

Engineering Mechanics 2 (2nd semester, BING)

• 4 ECTS
• Objectives. The lecture builds on the basics concepts of statics (Engineering Mechanics 1) and first extends the investigation of equilibrium states to plane trusses. The students can identify the axial forces in truss members and support forces by the method of section (Ritter) as well as by the nodal section method. The students learn to distinguish static and kinetic friction. Introduction of the basic concept of mechanical strain and stress leads over to the field of elastostatics. The students know the load-bearing behaviour of rods and beams and can describe it mathematically by means of the associated governing equations. They can quantify section properties that define tensile and bending stiffness of members. The students can perform predictions of stress states due to tension/bending and can identify location and magnitude of stress extrema. They can critically examine their result with respect to allowed stress states and safety considerations.
• Content. Plane trusses; Static and kinetic friction; Belt friction; Introduction to elastostatics: behaviour of straight rods and beams, stress and strain state; Governing equations: kinematics, equilibrium, material law; Tension and compression in straight rods; Bending of straight beams (Timoshenko, Euler-Bernoulli); Section characteristics: area moments, parallel axis theorem (Steiner), principal axis, non-symmetric bending; Maximum stress, design and safety concepts; Temperature loads.
• Evaluation. Written exam.

Engineering Mechanics 3 (3rd semester, BASI)

• 4 ECTS
• Objectives. The lecture continues the discussion of elastostatics from Engineering Mechanics 2 (BASI). The students are introduced to the behaviour of straight members subject to torque and the resulting stress and deformation states for various section geometries. The students know the mathematical formulation to kinematics, equilibrium and linear elastic material for the mechanical phenomena tension, bending, torsion and can solve the differential equations for given kinematic and static boundary conditions. The students are familiar with balancing the mechanical work of a system and understand the concept of virtual work. They comprehend the principle of virtual displacements as an alternative global equilibrium statement and the principle of virtual forces as an alternative global compatibility statement. The students know the difference between state lines and influence lines. The students obtain an introduction to second order stress theory, basic linear stability problems and model extensions for Euler-Bernoulli beams.
• Content. Torsion of straight members, closed and open sections; Comparison of the governing equations for compression/tension, bending, torsion and kinematic/static boundary conditions; Solution of the ordinary differential equations; Work and virtual work, principle of virtual displacements, principle of virtual forces, applications; State lines and influence lines; Second order stress theory, application: ropes; Linear stability analysis, application: buckling of beams; Continuously and elastically-supported beams and solutions.
• Evaluation. Written exam.

Structural Analysis 1 (2nd semester, BING)*

• 3 ECTS
• Objectives. The lecture introduces to the objectives and approaches to the analysis of civil engineering structures. Herein, the focus is on systematic and material-independent structural design and structural modelling. The students can, qualitatively and quantitatively, evaluate given structural systems and their load-bearing behaviour for given loading scenarios. The students know the theoretical foundations and acquire the competence to determine the force and deformation state of statically determinate models. They can identify systems that can undergo rigid body displacements using the pole plan and can determine these rigid body modes.
• Content. Role and tasks of structural analysis in structural engineering; Structural systems and their components, modelling structural components, modelling of connections and supports, modelling of loads; Connected beams and plane frame structures; Force and deformation quantities, continuity at connections; Method of sections, degree of static and kinematic indeterminacy; Governing equations of straight rods and beams (Euler-Bernoulli theory); State lines of force quantities (M,Q,N) and deformation (w) for statically determinate multi-span beams and frames; Kinematic underdeterminacy: pole plan and rigid body displacements for kinematic systems.
• Evaluation. Written exam.

Structural Analysis 2 (3rd semester, BING)*

• 4 ECTS
• Objectives. Using the foundations of elastostatics (Engineering Mechanics 2), the lectures introduces the terminology of mechanical work and establishes the basic principles of virtual work in the context of structural analysis: the principle of virtual displacements and the principle of virtual forces. The students comprehend these energy principles as alternative forms of the equilibrium state or deformation state at the system level. They can apply the PVD in order to determine force quantities and they can use the PVK for calculation of deformations. By executing the calculations manually the students can judge the physical and geometrical factors that determine the force/deformation state of a structure and can perform basic structural design optimisations. The students know the difference between state and influence lines and can construct and evaluate the influence lines for force and deformation quantities.
• Content. Mechanical work and work balance, virtual work; Principle of virtual displacements (PVD), determination of force quantities at statically determinate structures with the PVD; Principle of virtual forces (PVF), determination of deformation quantities at statically determinate structures with the PVF, calculation of bending deformation state lines; Influence lines and state lines, influence lines for force quantities (Land theorem), influence lines for deformation quantities (Maxwell/Betti theorem).
• Evaluation. Written exam.

Structural Analysis 3 (4th semester, BING)*

• 3 ECTS
• Objectives. This lecture provides the basis for estimation of the load-bearing characteristics and analysis of statically indeterminate structures using classical methods of structural analysis. The students are enabled to determine state lines for force and deformation quantities of statically indeterminate multi-span beams and plane frame structures using the flexibility and stiffness method. They know about the load-bearing behaviour of statically indeterminate structural systems and the importance of the stiffness distribution. In addition to the utilisation of classical manual calculation approaches the students are introduced to computer-based analysis of structures.
• Content. Repetition: Work and work principles, determination of the degree of static/kinematic indeterminacy; Flexibility method (Kraftgrößenverfahren): statically determinate principal systems, global equilibrium states and local deformation constraints, state lines of the statically indeterminate system, applications; Generalisation of the flexibility method and diagonalisation, deformation analysis with the reduction theorem; Stiffness method (Weggrößenverfahren): kinematically determinate principal system, global deformation states and local equilibrium constraints, simplification to the axially rigid case (Drehwinkelverfahren), applications; computer-based structural analysis.
• Evaluation. Written exam.

Plastic Hinge Theory (6th semester, BASI)

• 4 ECTS
• Objectives. This lecture introduces the load-factor method for determination of the limit state of structures, including the influence of the interaction of stress resultants and effects of second-order theory. Knowledge of the load-factor method and second-order stress theory constitute the foundation for comprehension of the current codes for structural engineering.
• Content. Introduction to the load-factor method; local load-bearing behaviour of various sections: moment-curvature relation, dissipation work; Load-capacity theorems, plastic limit state, kinematic method based on the principle of virtual displacements, determination of the limit load for frame structures, M-N-Q interaction; Calculation of deformations, second-order plastic hinge theory; Design of steel structures; Flow plasticity theory: flow rule and consistency condition, yield criteria.
• Evaluation. Written exam.

Bachelor Theses (BING & BASI)

Final applied theses at the bachelor level are offered in the following areas:

• Code-based design and analysis of typical civil engineering structures, e.g. bridges, pedestrian bridges, multi-storey buildings, hall structures, roof constructions
• Analytical mechanics and applications

Master Courses

Thin-Walled Structures (1st semester, MSCE)*

• 5 ECTS
• Objectives. The students know about the load-bearing behaviour of thin-walled structures. They are familiar with the fundamental mathematical modelling of plates and shells with emphasis on boundary conditions (restraints and loading) and stress/strain concentrations. The students know the basics of standard solution and analysis methods, especially finite element methods for thin-walled structures.
• Learning Outcomes. The students will be able to select the appropriate structural model for plane and curved thin-walled structures. They can perform the structural analysis of plane and curved thin-walled structures and are able to obtain a critical interpretation of the resulting stress distribution and displacements.
• Content. Recapitulation of 3D elastostatics and linear elasticity. Theory of plane thin-walled structures: (1) governing equations and in-plane membrane load-bearing behaviour of thin structures, influence of boundary conditions, trajectory of principal strains/stresses and dimensioning, plane strain/plane stress conditions, axisymmetric load-bearing structures. (2) governing equations and bending load-bearing behaviour of thin (Kirchhoff) and medium-thick (Reissner) plates, principal curvatures/moments and dimensioning, theory-dependent influence of boundary conditions. Orthotropic plates, folded plates, circular plates. Theory of curved thin-walled structures: (3) governing equations and combined load-bearing behaviour of shells of revolution, membrane theory and bending theory, extension to non-axisymmetric conditions. Based on the theory, the lecture complementarily discusses methods of finding closed and approximate solutions to the governing equations in displacement and displacement/stress form: solution of partial differential equations, application of the principle of virtual displacements and virtual stresses to thin-walled structures, ansatz functions of full-field support (deformation modes) and local support (finite elements). Discussion of the plausibility, quality and sensitivity of structural analysis results.
• Evaluation. Student team semester project with presentation and written report.

Finite Element Analysis of Structures (1st semester, MSCE)*

• 5 ECTS
• Objectives. Starting from basic strong-form governing equations of linear but also geometrically/physically nonlinear structural problems, the students will be able to obtain the associated (linearised) weak form on the basis of the principle of virtual work. They know about the most important steps of discretisation of geometry and physics, they are familiar with the standard (isoparametric) Lagrange-type elements in 1D, 2D and 3D.
• Learning Outcomes. The students can identify and understand the steps of pre-processing, element matrix computation, system matrix assembly, solution and post-processing in theory and source code (MATLAB). They are able to distinguish stress and stability problems and can perform reliable assessment of finite element analyses of linear and nonlinear structures. The students are familiar with the concept of the finite element method as a means of obtaining an approximate solution to the mathematical model equations (coupled ordinary/partial differential equations) associated with standard structural components such as trusses, beams, slabs and plates.
• Content. The focus of the course is on identifying (physics and mathematics) and processing (computer program implementation) the basic steps involved in a typical finite element analysis workflow from an academic point of view. (1) Introduction to MATLAB: Installation of Matlab Toolbox, Matlab concepts; (2) First steps with MATLAB: Walkthrough tutorial; (3) Introduction to FE as part of the design tool chain to structures, structural components; (4) Overview on governing equations for some structures (spring, bar, beam, rope, slab, plate, membrane, shell, solid); (5) Method of weighted residuals (trial function, residual, test function, integral form, weak form); (6) Discretisation of geometry (partitioning of the domain, meshing, local coordinate system, mapping, Jacobi matrix); (7) Discretisation of physics (local and global derivatives, isoparametric concept); (8) Numerical integration of the weak form (Gauss quadrature): element matrix and element force vector, assembly, system of linear algebraic equations, solution methods (direct, iterative); (9) Nonlinear problems: general approach via Newton-Raphson method, consistent linearisation; (10) Physically nonlinear structures (material nonlinearities) – nonlinear elasticity; (11) Geometrically nonlinear structures – nonlinear truss, rope, beam, plate; (12) Stability analysis of structures: formulation as eigenvalue problem, buckling load and buckling shapes.
• Evaluation. Assignments during the semester and written exam.

Structural Dynamics (2nd semester, MSCE & MSPC)*

• 4 ECTS
• Objectives. The students know the theoretical foundations of discrete and continuous (longitudinal, transversal and torsional in 1D continua, wave propagation in thin-walled structures) vibration problems and associated single- and multiple-degree of freedom systems. They can develop suitable models of two- and three-dimensional frame structures and know how to apply methods for the solution of the resulting system of equations of motion. The students know typical sources of structural excitation in civil and mechanical engineering and can perform first dynamic response analyses together with structural dimensioning based on the code (DIN).
• Learning Outcomes. The students will be able to develop appropriate structural models for selected constructions, perform the associated vibration analysis and its critical interpretation as well as to identify suitable modifications of structural designs in order to meet co-existing criteria such as safety, reliability and resource efficiency.
• Content. Periodic and non-periodic vibration; modelling of rigid-body systems and continuous flexible structures (rods, beams, torsion, frame structures, plane structures); derivation of the set of equations of motion: synthetic and analytic method; rotational motion/constrained motion; linearisation and solution of the equation of motion; free and forced vibration of undamped and damped structures; modal analysis and modal synthesis; modal reduction. Exemplarily, the following engineering applications can be discussed in detail: (1) earthquake engineering: seismic excitation, response spectrum method, (2) wind engineering: wind and fluid flow excitations, flow-induced vibrations, (3) bridge engineering: dynamic railway excitation, (4) damping: active and passive damping devices (5) rotor dynamics, aerodynamic forces: application to wind turbines.
• Evaluation. Student team semester project with presentation and written report.

Master Theses (MSCE & MSPC)

Final scientific theses at the master level are offered in the following areas:

• Statics and dynamics of thin-walled structures
• Approximate solution methods, e.g. finite element methods
• Computational mechanics

Doctoral Training

Introduction to Fluid-Structure Interaction

• Objectives. The lecture introduces the basics of interactions of structures and fluids. Based on an overview of typical interaction phenomena from the fields of civil engineering, mechanical engineering and aerospace, suitable instruments for their characterisation and classification are developed. The presentation first deliberately focuses on the structure and discusses the influence of a surrounding or enclosed flow field on the static and dynamic response behaviour of the structure.
• Content. The most relevant structure and fluid models are introduced and their coupling along a common boundary is discussed. On the structural side, this concerns simple rigid body models, flexible structures such as beams and plates, as well as shells with combined loading from membrane and flexural load-bearing behaviour. On the fluid side, incompressible friction and vortex-free flows (potential flow), viscous flows (Navier-Stokes) and compressible (acoustic) fluids are considered. Based on the respective mathematical model equations, possible strategies for coupling the individual fields are developed. Since the involved basic mathematical equations are typically not accessible to a closed solution for more complex tasks in the technical field, approximation methods for fluid-structure interaction problems are discussed in the lecture. For the discrete description of structure and fluid, finite element techniques are presented and numerical strategies for fulfilling the equilibrium and compatibility conditions at the coupling interface are presented. Depending on the previous knowledge of the participants, a MATLAB implementation can be integrated into the course to demonstrate the above models and strategies for fluid-structure interaction problems.
• Course Material. Slides, written material, lecture notes and MATLAB demonstrations.

Extended Finite Element Method (XFEM) [taught with Prof. Fries, TU Graz]

• Objectives. Standard numerical methods like the FEM and FVM are widely established in today’s engineering practice. They are well-suited for the approximation of smooth solutions. However, in the real world, there is an infinite number of examples where field quantities do not behave smoothly but show jumps, kinks, singularities, etc. For example in solids, stresses and strains are discontinuous along material interfaces and singular at crack tips. In fluids, pressure and density change rapidly near shocks and the velocity gradient can be extremely large in boundary layers. In contrast to standard numerical methods, the XFEM enables the approximation of non-smooth solutions with optimal accuracy. This is achieved by a local enrichment of the approximation space such that the special solution properties are considered appropriately. The XFEM is in the focus of intensive research activities and is currently realised in commercial finite element software tools. This seminar is designed for graduate and doctoral students as well as developers from industry with interest in the XFEM and its wide applications.
• Content. Overview of the course topics: (1) Basics of XFEM I: weighted residuals, enriched approximation; (2) Basics of XFEM II: properties of enriched approximations; (3) Implementation of XFEM: numerical integration, assembly, post-processing; (4) Tutorial A: implementation in MATLAB, 1-D: diffusion problem; (5) XFEM in structural mechanics I: bi-material problems, corrected XFEM; (6) XFEM in structural mechanics II: cracks and crack growth; (7) XFEM in structural mechanics III: finite deformation, non-linear materials; (8) Tutorial B: implementation in MATLAB, 2-D: inclusions and cracks; (9) XFEM in fluid mechanics: transient problems, moving fronts, two-fluid flows; (10) XFEM in multi-physics: fluid-structure interaction; (11) Background of XFEM: partition-of-unity method, intrinsic XFEM.
• Course Material. Comprehensive manuscript (lecture notes), survey papers by the lecturers, recent manuscripts and a literature overview, computer code with a MATLAB implementation.

Last updated on: 11 Apr 2020

Luxembourg

• Doctoral Training Unit Data-driven computational modelling and applications (DTU DRIVEN) funded by FNR (PRIDE)
• Research Group Eco-construction for sustainable development (ECON4SD) funded by EU/H2020
• Research and Industrial Transfer Project Conceptualisation of a computational and data engineering hub for Luxembourg (CDE-HUB) funded by EU/H2020

Europe and International

• International Research Exchange Programme Scientific excellence and technology-transfer capacity in data-driven simulation of the University of Luxembourg (H2020 DRIVEN) funded by EU/H2020
• Cost Action European Model Reduction Network (EU-MORNET) funded by EU/H2020

Last updated on: 11 Apr 2020