Teaching

An overview of previously taught exercise lectures.

Engineering Mechanics I: Statics of Rigid Bodies

This course, intended for first-semester engineering students, introduces the fundamental principles of engineering statics. The course covers the following topics:

Concepts of force and moment
Types of supports, statically determinate structures
Conditions of static equilibrium in two- and three-dimensional systems
Centroids, distributed line loads, and surface loads
Truss structures and Ritter’s method of sections
Beam analysis: shear forces, bending moments, and their differential relationships
Principle of superposition
Static and kinetic friction
Conservative forces and potential energy
Stable and unstable equilibrium

Learning Outcomes: Upon successful completion of the course, students are able to apply the fundamental concepts governing the behavior of engineering structures using the rigid-body model. Based on a small set of fundamental physical principles, they can analyze individual rigid bodies as well as systems of rigid bodies and apply systematic engineering methods to solve statics problems. They are also able to apply these principles to model and analyze engineering structures and technical systems.

Engineering Mechanics II: Strength of Materials

Building on the concepts introduced in Engineering Mechanics I, this course introduces the fundamental principles of strength of materials and elasticity. The course covers the following topics:

Bars under axial loading: tension, compression, stress, strain, Hooke’s law, governing differential equations, and buckling
Statically determinate and indeterminate structures
Multiaxial states of stress and strain, principal stresses, and Mohr’s stress circle
Beams: Euler–Bernoulli beam theory, second moments of area, bending and shear stresses, differential equations of the elastic curve, and torsion
Principle of virtual work and methods based on virtual forces and displacements

Learning Outcomes: Upon successful completion of the course, students are able to apply the fundamental concepts of strength of materials and elasticity to analyze the mechanical behavior of structural elements. They can describe stress and strain states and relate them through constitutive laws to determine deformations under combined loading conditions involving axial forces, bending, shear, and torsion. Students are able to analyze both statically determinate and statically indeterminate structures using equilibrium and energy methods, including the principle of virtual work. They are also able to evaluate the stability of elastic structures through buckling analysis and apply these methods to solve engineering problems in structural engineering.

Engineering Mechanics III: Dynamics

Building on the concepts introduced in Engineering Mechanics I and II, this course introduces the fundamental principles of classical dynamics. The course covers the following topics:

Kinematics of particles and systems of particles
Kinetics of particles and systems of particles: Newton’s laws of motion, equations of motion, work–energy principle, and conservation of energy
Momentum principle and impact problems
Kinematics and kinetics of rigid bodies: mass moments of inertia, center of mass principle, and angular momentum principle
Systems of rigid bodies: synthetic approaches (method of sections) and analytical methods (Lagrange’s equations)
Introduction to vibration mechanics: modeling free, damped, and forced vibrations

Learning Outcomes: Upon successful completion of the course, students are able to apply the fundamental concepts, laws, and methods of classical dynamics. They can formulate equations of motion using both synthetic and analytical approaches and analyze the dynamic behavior of technical systems. Using principles of vibration theory, students are able to describe oscillatory phenomena.

Dynamics of Structures

Building on the concepts introduced in Engineering Mechanics III, this course focuses on the analysis of structural vibrations in engineering systems. The course covers the following topics:

Kinematics and fundamentals of vibration theory
Harmonic, periodic and non-periodic vibrations
Harmonic analysis and frequency-domain representation
Single-degree-of-freedom systems: modeling, undamped and damped free vibrations, impulse excitation, harmonic excitation, and transfer functions
Multi-degree-of-freedom systems: formulation of equations of motion, natural frequencies, mode shapes and modal analysis

Learning Outcomes: Upon successful completion of the course, students are able to describe and analyze vibration phenomena in engineering structures. They can identify the causes of structural vibrations and apply appropriate mechanical models and analytical methods to evaluate dynamic behavior. Students are able to formulate and solve equations of motion for single- and multi-degree-of-freedom systems, determine natural frequencies and mode shapes.

Computational Structural Dynamics

Building on the fundamentals of structural dynamics and numerical methods, this course introduces advanced approaches for the simulation and analysis of dynamic mechanical systems. The course covers the following topics:

Discrete mechanical systems in linear structural dynamics
Hamilton’s principle and its relation to Lagrange’s equations, Hamilton’s equations and the principle of virtual work
Numerical time integration methods (including the implicit and explicit Euler method, midpoint method, generalized-alpha and Newmark method)
Structure-preserving methods for the stable integration of nonlinear dynamic systems (e.g. variational integrators and energy-momentum methods)
Noether theorem and discrete conservation principles
Analysis of accuracy and numerical stability of time-stepping schemes
Computational implementation of selected integrators using MATLAB/Python

Learning Outcomes: Upon successful completion of the course, students are able to use and evaluate common time-stepping methods in structural dynamics. They can assess the properties of numerical methods with respect to accuracy and numerical stability. Students are able to implement numerical algorithms computationally and apply them to analyze dynamic engineering systems.

Basics of Finite Elements

This course introduces the theoretical foundations and practical implementation of the finite element method (FEM) for solving engineering boundary value problems. The course covers the following topics:

Variational formulation of 1D, 2D, and 3D boundary value problems and weak form (e.g., linear elasticity, heat conduction)
Galerkin method
FEM: Test functions, shape functions, continuity requirements, and domain discretization
Element stiffness matrices and global assembly
Isoparametric, Lagrangian finite elements
FEM for beam bending (Euler-Bernoulli & Timoshenko), discussion of transverse shear locking and remedies
Rayleigh–Ritz method
Numerical integration and accuracy of finite element approximations
Implementation of finite element methods

Learning Outcomes: Upon successful completion of the course, students are familiar with the variational foundations of the FEM and can apply Lagrangian finite element formulations of different approximation orders to one-, two-, and three-dimensional problems in linear elasticity and heat conduction. Students understand that the finite element method provides an approximate solution to boundary value problems and are aware of its assumptions and limitations. They are prepared to use commercial finite element software effectively and to apply FEM concepts to practical engineering problems.

Finite Elements in Solid Mechanics

This course introduces advanced static and dynamic finite element formulations including mixed approaches for linear and nonlinear continuum mechanics problems. The course covers the following topics:

Multi-field variational formulations (Hu–Washizu and Hellinger–Reissner) of linear elasticity
Mixed finite element formulations based on additional approximations of strains and stresses (including Enhanced Assumed Strain (EAS) and Pian–Sumihara hybrid elements)
Extension to geometrically and materially nonlinear problems
Extension to (quasi-)incompressible problems with related advanced mixed FEM
Volumetric locking and its remedies
Extension to dynamics and time-dependent problems
Practical implementation in MATLAB

Learning Outcomes: Upon successful completion of the course, students are able to distinguish and classify different mixed finite element formulations and understand their underlying multi-field approaches and variational principles. They can conduct a FE analysis of both linear and nonlinear problems, in static and dynamic cases, involving geometric and material nonlinearities. Students are able to evaluate the suitability of different mixed finite element formulations for specific engineering applications and gain practical experience in implementing these methods.