Peter Wriggers

Dieses Lehrbuch zur Technischen Mechanik behandelt die Starrkörperstatik, die Elastostatik und die Kinetik kompakt in einem einzigen Band. Es werden die wesentlichen Grundgesetze der Mechanik und die Fähigkeiten zum Formulieren und selbstständigen Lösen von Ingenieurproblemen vermittelt. Neben Herleitungen der theoretischen Zusammenhänge werden motivierende Beispiele mit ausführlichem Lösungsweg dargestellt. Viele Übungsaufgaben regen zum eigenständigen Studium an. Hilfsmittel zum Lösen der Aufgaben sind im Anhang zusammengestellt, ebenso Stichwortverzeichnis sowie eine deutsch-englische Vokabelübersicht. Für die 2. Auflage wurde das Buch gründlich durchgesehen und im Kapitel Schwingungen überarbeitet. Weitere Informationen im Internet unter www.tm-kompakt.de

Contact mechanics has its application in many engineering problems. No one can walk without frictional contact, and no car would move for the same r- son. Hence contact mechanics has, from an engineering point of view, a long history, beginning in ancient Egypt with the movement of large stone blocks, over ?rst experimental contributions from leading scientists like Leonardo da Vinci andCoulomb, to today’s computational methods. In the past c- tact conditions were often modelled in engineering analysis by more simple boundary conditions since analytical solutions were not present for real world applications. In such cases, one investigated contact as a local problem using the stress and strain ?elds stemming from the analysis which was performed for the entire structure. With the rapidly increasing power of moderncomp- ers, more and more numerical simulations in engineering can include contact constraints directly, which make the problems nonlinear. This book is an account of the modern theory of nonlinear continuum mechanics and its application to contact problems, as well as of modern s- ulation techniques for contact problems using the ?nite element method. The latter includes a variety of discretization techniques for small and large def- mation contact. Algorithms play another prominent role whenrobustand- cient techniques have to be designed for contact simulations. Finally, adaptive methods based on error controlled ?nite element analysis and mesh adaption techniques are of great interest for the reliable numerical solution of contact problems.

This book contains the numerical methods, mathematical analysis, algorithms, software aspects and comparative results of a six year joint project of nine German University institutes, supported by the German National Science Foundation (DFG). It covers new progress for efficient and reliable error estimates mainly of the Finite Element Method for non-linear problems in solid mechanics, as well as efficient re-meshing techniques and solution algorithms. Topics covered include: *Elastoplastic deformations and contact problems *Shear localization of inelastic deformations *Thin-walled structures *Elastodynamics The authors, all experts in computational mechanics, provide a wealth of new ideas for the next generation of software for adaptive finite elements, which will be of great interest to industry. Each chapter includes the state of the art, comparisons between different methods and the mechanical and mathematical background of the methods addressed. Practising engineers, researchers and students in engineering, applied mathematicians and computer scientists will find new material for developing, maintaining and applying finite element algorithms which reach new heights of approximation quality.

Boundary value problems involving contact are important for industrial applications in both mechanical and civil engineering, such as structural foundations, bearings, metal forming processes, rubber sealings, drilling problems, crash analysis of cars, rolling contact between car tyres and the road, cooling of electronic devices, and many more. Other applications are related to biomechanical engineering design, where human joints, implants or teeth are considered. Due to this variety, contact problems today are combined either with large elastic or inelastic deformations, including time-dependent responses. Thermal coupling may also have to be considered, and even stability behaviour has to be linked to contact, such as wrinkling arising in metal forming problems. The topic of computational contact is described in depth here, providing different formulations, algorithms and discretisation techniques for contact problems that have been established in the geometrically linear and nonlinear ranges. This book provides the necessary continuum mechanics background. Special geometrical relations needed to set up the contact constraints are derived, and constitutive equations stemming from tribology which are valid at the contact interface are discussed in detail, without going into a numerical treatment. Solid and beam contact is considered, as is contact of unstable systems and thermomechanical contact. The algorithmic aspects cover a broad range of solution methods. Additionally, adaptive discretisation techniques for contact analysis are presented as a modern tool for engineering design simulations. This book: *applies to a wide variety of industrial applications, *starts from a sound continuum mechanics background, *introduces new discretisation techniques and algorithms, and *includes thermo-mechanical considerations and adaptive methods. Computational Contact Mechanics has been written not only for graduate, Masters and PhD students, but also for engineers in the car, tyre and packaging industries who simulate contact problems in practical applications and need to understand the theoretical and algorithmic background of contact treatment in modern finite element systems.

Die Anwendung der Finite-Element-Methode auf nichtlineare technische Probleme hat in den letzten Jahren - auch wegen der stark angestiegenen Rechnerleistung - erheblich zugenommen. Bei nichtlinearen numerischen Simulationen sind verschiedene Aspekte zu berücksichtigen, die das Wissen und Verstehen der theoretischen Grundlagen, der zugehörigen Elementformulierungen sowie der Algorithmen zur Lösung der nichtlinearen Gleichungen voraussetzen. Hierzu soll dieses Buch beitragen, wobei die Bandbreite nichtlinearer Finite-Element-Analysen im Bereich der Festkörpermechanik abgedeckt wird. Das Buch wendet sich an Studierende des Ingenieurwesens im Hauptstudium, an Doktoranden aber auch an praktisch tätige Ingenieure, die Hintergrundwissen im Bereich der Finite-Element-Methode erlangen möchten.