# Mechanics

## Why mechanics?

Mechanics is the oldest branch of physics – and the foundation for many highly topical questions in current engineering research. Mechanics is the study of the motion and deformation of bodies under the action of forces. Even in ancient times this issue has occupied and fascinated scientists for very practical reasons: heavy loads had to be lifted and carried, buildings were erected or military equipment designed. Classical mechanics, as it is taught today, is based on Newton’s laws, which describe the principle of inertia, the relationship between acceleration and force and the effect of force and counterforce. The development of mechanics has always been closely linked to developments in mathematics, e.g. the integral and differential calculus, vector calculus or the calculus of variations.

In particular, the development of numerical methods for solving differential equations and the rapid improvement of computing power have opened up new fields of application for Computational Mechanics. Today, mechanical simulations are irreplaceable in industrial design and manufacturing processes: the crash behavior of entire cars is modeled on the computer, as well as laser welding of pipes or the formation of micro-cracks in composite materials. The increasing demands on materials, components and structures are constantly posing new challenges to computational mechanics, such as the development of problem-specific numerical methods and algorithms or the development of mathematical models to describe complex material behavior. This requires both a sound knowledge of the basics of mechanics and mathematics, as well as the ability to implement the resulting models. For this reason, the TAF ‘Mechanics and Dynamics’ has been established.

In your Bachelor’s study, you will at first learn the fundamentals of mechanics: Statics, Elastostatics and Dynamics of Rigid Bodies. You will also learn the basics of an important numerical method in engineering, the Finite Element Method. These courses are supplemented by lectures on fluid mechanics or vibration theory. In the master program advanced courses on computational mechanics (nonlinear finite element method, material modeling and simulation) and continuum mechanics are offered. Courses on particular fields of mechanics (biomechanics, fracture mechanics, damage mechanics, …) complete the study plan.

The later career fields for graduates with a good knowledge in mechanics are manifold: mechanical engineering, automotive engineering, aerospace engineering, environmental engineering, chemical engineering, civil engineering, medical engineering, materials engineering, process engineering, …

## Content of the Bachelor Program

### Statics, Elastostatics and Strength of Materials/ Dynamics

The module Statics, Elastostatics and Strength of Material deals with the statics of rigid bodies (stereo statics) and the statics of deformable bodies (elastostatics). After the mechanical fundamentals and definitions, planar and stereo structures are regarded, reaction forces and momentums as well as internal force variables are introduced. Besides friction and the principle of virtual work, the description of characteristic area properties (center of gravity, moment of inertia) is regarded, providing a basis for the following elastostatics. Introducing the local loads, stresses and strains, the lecture leads to the stress and deformation of straight slender beams, loaded by tension, bending, torsion and shear forces. Finally, basic energy methods are shown and an introduction to the theory of strength of materials is given. The module Dynamics deals with kinematic and kinetic of mass points, systems of mass points and rigid bodies. Based on the principles of linear and angular momentum, the conservation equations are derived and discussed. The lecture ends with an introduction to the theory of vibrations for systems with one degree of freedom.

### Mechanical Vibrations

The module Mechanical Vibrations deals with technological relevant mechanical vibration problems. To this end, firstly the equations of motion have to be formulated based on an appropriate physical/mathematical modelling. Thereby the focus is on discrete systems with one and multiple degrees of freedom. The solution of the resulting (ordinary) differential equations allows the analysis and assessment of technological systems that are susceptible to mechanical vibrations. The module Multi body Dynamics extends these treatments to the case of multi body systems.

### Finite Element Methods

The module Finite Element Methods provides a general framework for the computational solution of boundary value problems from various different engineering applications. In the present lecture, we introduce its theoretical background, discuss its characteristic features and illustrate its algorithmic realization. Starting with a one dimensional model problem, we discuss the strong form of the governing equations, the derivation of the related weak form and its computational solution. We then turn to the evaluation of more complex problems, such as heat conduction, bending problems or the classical elasticity problem. In addition, finite element specific aspects like the isoparametric concept or numerical integration will be addressed. Computational examples and related MATLAB codes will be provided throughout to illustrate the algorithmic realization of the Finite Element Method.

## Study plans

Can be found on the CE-Homepage under important documents.