Studies and Teaching

The course begins by covering the fundamentals of the statics of rigid bodies (stereostatics). The focus is on the equilibrium conditions for forces and moments, as well as their application to beam and truss structures. The goal is to calculate external and internal forces. The course also covers problems involving the calculation of centers of volumes, areas, or lines, as well as the adhesion of bodies to contact surfaces. The second part of the course provides an introduction to the statics of elastically deformable bodies (elastostatics). Here, a foundation is established for performing classical strength-of-materials calculations for engineering structures. The course begins by covering basic loading situations such as tension and compression, straight and oblique bending, and torsion. Key concepts and relationships such as stresses, strains, principal axes, and Hooke’s law are introduced. For simple structural components, local stresses and displacements are calculated, e.g., in the form of the elastic bending line.

Building on the course “Engineering Mechanics 1,” this course continues the study of elastostatics. To address multiaxial stresses, strength hypotheses and equivalent stresses are introduced. Finally, the course provides an introduction to stability theory and the buckling of beams. The second part of the course provides an introduction to the kinematics and kinetics of point masses. In addition to the dynamic equilibrium conditions and d’Alembert’s principle, the course covers the work and energy theorems of mechanics. This is followed by an introduction to the theory of free, damped, and forced oscillations. Finally, the kinematic and kinetic fundamentals are extended to rigid bodies, with a general, tensor-based representation being taught. The goal is to derive equations of motion for constrained multi-body systems using the method of sections.

This module builds on the courses “Engineering Mechanics 1” and “Engineering Mechanics 2” and is obligatory for the specialization “Modellierung und Simulation in der Angewandten Mechanik.” The module begins with an introduction to various energy methods in mechanics, in particular the Ritz method, Maxwell and Betti’s reciprocity theorem, and the theorems of Castigliano and Menabrea. In addition, stability problems are examined in depth. Castigliano’s theorem is used to calculate local displacements in a structure and to efficiently analyze statically indeterminate structures, both internally and externally. Lagrange’s formulation of d’Alembert’s principle provides, as a special case, the principle of virtual work in statics. Further topics in elastostatics focus on the torsion of thin-walled structures of arbitrary cross-sections and shear forces, the calculation of shear centers, and the theory of shear-compliant (Timoshenko) beams. The course concludes with an introduction to the finite element method.

Course announcement WiSe 2026/27

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.

Course announcement SoSe 2026

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 exploited in 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.

Course announcement WiSe 2026/27

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.

Course announcement WiSe 2026/27

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 and 2, 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 the Linear Continuum Mechanics module, is generalized for arbitrary problems. The lecture ends with an introduction to plane elasticity theory.

Course announcement SoSe 2026

This course covers the fundamentals of structural fatigue strength. This includes both the theoretical strength analysis of components and the fundamentals of experimental structural fatigue strength. The goal is to evaluate operational loads and translate them into test conditions, as well as to independently perform computational strength and service life analyses.

Course announcement WiSe 2026/27

Due to their complexity, initial and boundary value problems that arise in practice usually cannot be solved analytically. The first numerical solution methods were developed in the middle of the last century. Due to the continuous advancement of computing power, numerical calculation methods have become indispensable in various fields of engineering today. Responsible use of the available computational methods requires a deeper understanding of the underlying principles. Only then can these methods be applied correctly and meaningfully, and their results interpreted appropriately.

Using simple mechanical problems as examples, this course provides an introduction to numerical mechanics. Building on initial and boundary value problems already familiar from Engineering Mechanics modules, students are taught the tools and methods for solving these problems numerically. In addition to an introduction to the one-dimensional finite element method (FEM), numerical methods for time integration are presented. Examples include truss structures, shear-rigid and shear-flexible beams, the mathematical pendulum, and the free fall of a point mass taking air resistance into account.

Course announcement SoSe 2026