Studies and Teaching

First, the fundamentals of the statics of rigid bodies are taught. The focus is on the equilibrium conditions for forces and torques and their application to beam and bar structures. The aim is the calculation of external and internal forces. Problems of the calculation of volume, surface or line centers or centers of gravity and the subject of contact/friction are also dealt with. In the second part of the lecture, an introduction to the kinematics and kinetics of mass points is given. In addition to the dynamic equilibrium conditions and d'Alembert's principle, the working and energy theorems of mechanics are treated. In the last part of the lecture, an introduction to the theory of free damped and forced oscillations for point masses is given.

This lecture is one unit together with the course Engineering Mechanics 1. First, the theory of oscillations with one degree of freedom is completed and then an outlook on oscillations with a finite number of degrees of freedom is given. Then, the extension of the kinematic and kinetic basics to rigid bodies takes place, where a general tensorial representation method is taught. The goal is to establish equations of motion for multibody systems using the body cut principle. The second part of the lecture is an introduction to the fundamentals of elastostatics. Here, a basis is created for carrying out classical strength calculations for technical structures. Basic stresses such as tension/compression, straight and oblique bending and torsion are dealt with. Central terms and relationships such as stresses, distortions, principal axis systems or Hooke's law are introduced. For simple structural components, local stresses and displacements are calculated, e.g., in the form of the bending line. For the treatment of multiaxial loads, strength hypotheses are taught. The lecture ends with an introduction to stability theory and column-buckling of beams.

This lecture is based on the courses Engineering Mechanics 1 and 2, however represents an independent unit. First, the basics of stability theory are deepened using the buckling of rods as an example. By introducing a higher order buckling differential equation, more general problems than Euler buckling can be solved. Then, an introduction to various energy methods of mechanics is given. In elastostatics, the Ritz method, the theorem of Maxwell and Betti, and the theorems of Castigliano and Menabrea are treated. The objectives are to calculate local displacements in a structure and to treat internally and externally statically indeterminate structures. In kinetics, d'Alembert-Lagrange's principle and Lagrange equations of 2nd kind are treated to establish equations of motion in generalized coordinates. Other contents of the lecture deal with torsion of thin-walled non-circular cross-sections and shear. The lecture ends with an introduction to the theory of plane structures using circular disks and plates as examples.

The aim of the lecture is to teach concepts for the calculation of geometrically nonlinear mechanical boundary value problems. General basics of continuum mechanics, e.g., balance equations for momentum, angular momentum, mass, energy and entropy in global and local form are also treated. First, there is a review of mathematical basics, in particular tensor analysis and algebra in different notations. Then, different viewpoints of the kinematics of large deformations are taught and the associated deformation and strain tensors and their rates of change are introduced. In the treatment of the kinetics of the continuum, different approaches to the description of mechanical stresses in large deformations are explained. The lecture concludes with a thermodynamically based introduction to materials theory.

Lecture announcement

In fracture mechanically motivated strength calculations, crack-like defects are assumed in structural components. Compared to an evaluation based on local stress concepts, as applied in classical strength theory, strength reserves can be better utilized in the implementation of lightweight design concepts and failure probabilities can be reduced. The aim of the lecture is to impart basic knowledge and numerical methods for fracture mechanics strength analysis. Starting with an energy balance on a body with a crack, the concept of energy release rate is first discussed. This is followed by an introduction to the theory of mechanics in material space, which finally leads to the formulation of path-independent conservation integrals. Cohesive zone models provide an alternative approach to fracture mechanics strength analysis. Finally, the calculation of field quantities in the cracked component and the K-concept follow from considerations of classical elasticity theory in complex function space. In the last part of the lecture, different numerical methods for computer-aided fracture mechanics analyses are explained and subsequently practiced in a computer lab.

Lecture announcement

In this lecture, fundamentals of continuum mechanics are generalized with respect to a treatment of multifield problems. These are boundary value problems which are defined by electric, magnetic and thermal variables in addition to stresses and strains as the mechanical state variables. The most general form of coupling between the different field variables is always assumed. For technical applications, the fundamentals taught are always relevant when, for example, the mechanical performance is influenced or even controlled by thermal, magnetic or dielectric properties or processes of the material. The lecture first includes a presentation of the physical fundamentals of multifunctionality. Then, the basic equations of mechanics, electrodynamics, and calorics are derived and discussed in the context of a multifield theory. A generalized thermodynamic theory of materials provides the basis for deriving constitutive laws to describe field couplings and multifunctionality at the phenomenological level. In addition to analytical solutions for simple coupled field problems, the fundamentals for numerical treatment using the FEM are explained. At the end of the lecture, an outlook on the principle of multiscale modeling is given.

Lecture announcement

The lecture is divided into two parts. First, there is an introduction to rational or analytical mechanics. After a short presentation of Newtonian mechanics, which contains some additions compared to the state of the lectures Engineering Mechanics 1-3, first Lagrangian and then Hamiltonian mechanics are treated in excerpts. Basic concepts like holonomic and non-holonomic constraints or virtual displacements are deepened. The structure of theoretical mechanics is presented in detail from the principle of d'Alembert/Lagrange via the Lagrangian equations of the 1st and 2nd kind to the principle and the canonical equations of Hamilton. In the second part of the lecture the basics of analytical mechanics are applied to problems of deformable bodies with continuous mass density, i.e., continuum mechanics problems. In addition to Hamilton's principle, other variational principles are introduced, as well as the method of weighted residuals. The Ritz method applied to stability problems in Engineering Mechanics 3 is generalized for arbitrary problems. The lecture ends with an introduction to plane elasticity theory.

Lecture announcement

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