L.104.22220 Finite-Element-Method 1

Instructors: Dr. Ismail Caylak

Event type: Lecture

Org-unit: Maschinenbau

Displayed in timetable as: FEM1

Hours per week: 2

Language of instruction: German

Min. | Max. participants: - | -

Requirements and recommendations:
Basic knowledge in mechanics and mathematics

Aim of the event:
Many problems of mechanical engineering lead to partial differential equations, which in most cases cannot be solved by analytical methods due time restrictions or inaccuracy. Among different numerical procedures the finite element method is the most efficient one for problems in fluid mechanics, thermodynamics, elastomers, bio mechanics, dynamics, metal forming, electronics and further engineering fields. Nowerdays most computer centres of universities and engineering offices in industry make use of commercial programs like ABAQUS, ANSYS or MARC. For example modern daily engineering work in car industry, tyre industry or gas turbine industry would be impossible to do without the finite element method. The lecture provides the basic approach of the method for problems of elasticity, heat or fluid mechanics. In the exercises specific attention is paid to the use of commercial program systems for pre- and postprocessing. Examples of thermal mechanical problems of gasturbine industry are treated.

Target group:
Students of mechanical engineering, Techno mathematics, Physics, Informatics

Contents:
Problems of mechanical engineering
- Elastic problems (beams, plane problems, 3-dim structures)
- Stationary heat problem
- problems of fluid mechanics

One dimensional finite element formulation
- Galerkin method
- The FEM as approximation method, "local" and "global" approach of FEM (element stiffnis matrix and System stiffness matrix), properties of matrices

Two dimensional finite element formulation
- Galerkin method
- The FEM as approximation method as a "local" approach (element stiffness matrix and System stiffness matrix), properties of matrices
- The isoparametric concept
- Application to mechanical and thermal problem

Introduction to mixed formulations
- Deficiencies of standard FE-method ("Volume-locking", "Shear-Locking")
- Mixed element formulations

Introduction into adaptive methods
- A priori and a posteriori error estimators
- Problems of elasticity and heat

Applications of FEM in Pre- und Post-Processing
- Pre-processing of simple geometrical structures with ABAQUS CAE
- Variation of materials, element types, meches
- FEM-analysis of stationary heat problem, mechanical problem
- Post-Processing, critical assessment of "coloured figures", comparison with analytical methods
- Vergleich mit analytischen Lösungen

Contact person:
Prof. Mahnken, Dr.-Ing. Ismail Caylak

Literature:
O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, 5th edition, Butterworth-Heinemann, 2000

Supplementary events:
see catalogue for course on material science