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Instructors: Prof. Dr. Rolf Mahnken M.Sc.
Event type:
Lecture
Org-unit: Maschinenbau
Displayed in timetable as:
EM
Hours per week:
2
Language of instruction:
German
Min. | Max. participants:
- | -
Requirements and recommendations:
Basic knowledge in mechanics and mathematics
Aim of the event:
The assessment of failure for materials in mechanical engineering requires in most cases knowledge about the three dimensional elastic stress and strain field. In this way e.g. the failure properties of ceramics are investigated. Other materials exhibit nonlinear elastic effects, such as polymeres and rubbers in car tyres. In order to achieve a realistic simulation the theory of linear elasticity has to be enhanced by a nonlinear theory. Futhermore the consideration of thermal effects is of great practical interest.
For approximative solution of the resulting thermo-mechanical field equations the basic principles of numerical approaches within the finite element method are introduced. Real problems are solved with the finite element program ABAQUS within the accompanying exercises.
Many materials occuring for example in car tyres exhibit non-linear elastic effecs, where polymeres and rubbers are typical examples. In order to achieve a more realistic simulation the theory of linear elasticity has to be replaced by a nonlinear theory. To this end in the lecture the basic principles of continum mechanics are formulated. Fundamental equations of the theory of elasticity are formulated, and techniques for its solution are derived.
Target group:
Students in mechanical engineering, industrial engineering, techno mathematics, physics and informatics
Contents:
- Stress tensor, Cauchy theorem, principle stresses
- displacement vector, strain tensor,
- Axioms of continuum mechanics, equilibrium equations
- constitutive laws in linear theory of elasticity (isotropy, anisotropy)
- strain energy of an elastic solid,
- Strong and weak forms of equilibrium
- Galerkin Ansatz for the finite-element-method
Contact person:
Prof. Mahnken
Literature:
Eschenauer, H.; Schell, W.: Elastizitätstheorie Bd 1,2; Wissenschaftsverlag Mannheim, Wien, Zürich 1981, 1984,
Hahn, H.G.: Elastizitätstheorie; Teubner-Verlag, Stuttgart 1985
Gross, D. et al.: Technische Mechanik 4, Springer Verlag, Berlin Heidelberg 1993
Mal, A.K.; Singh, S.J.: Deformation of Elastic Solids, Prentice-Hall-Verlag 1991
Supplementary events:
see catalogue for course on material science
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