Finite Elementes
Short Description
In the lecture Finite Elements the theoretical basics and their numerical implementation by means of the Finite Element Method (FEM) are to be worked out. As a basis, the method of weighted residuals and the scribing process are presented. Based on this, the weak form of elliptical boundary value problems and their basic derivation is shown. Using simple one-dimensional examples such as members or bars, the area discretization with the FEM of common differential equations is clearly explained. The introduction of different two-dimensional element types also allows the treatment of partial differential equations. Central terms such as stiffness matrix, incidence matrix, test functions, attachment functions or continuity requirements are introduced clearly and comprehensibly. The basics of elasticity theory can be used to treat general two-dimensional solid state problems. The topics covered include flat distortion and stress state, subintegration, mixed formulation and incompressibility. Furthermore, important aspects of the underlying numerical mathematics such as numerical integration are shown. The theory can be deepened in classroom exercises using examples. In addition, aspects of practical programming are comprehensibly explained in the exercises and can be traced in computer exercises.
Themens
- Weighted residuals method, scribing method
- strong and weak form of elliptical boundary value problems
- FE Discretization of ordinary and partial differential equations
- Bar, beam and membrane elements
- theory of elasticity
- Continuum elements of different order
- isoparametric concept
- numerical integration
- underintegration
- mixed element formulation
- incompressibility
- FE program technology.
Prerequisites
- Basic Lectures in Technical Mechanics
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Old examinations
- Summer Semester 17 / Solution
- Winter Semester 16/17 / Solution
- Summer Semester 16 / Solution
- Winter Semester 15/16 / Solution
- Summer Semester 15 / Solution
- Winter Semester 14/15 / Solution
- Summer Semester 14 / Solution
- Winter Semester 13/14 / Solution
- Summer Semester 13 / Solution
- Winter Semester 12/13 / Solution
- Summer Semester 12 / Solution
- Wintersemester 11/12 / Solution
- Summer Semester 11 / Solution
- Winter Semester 10/11 / Solution
- Summer Semester 10 / Solution
- Winter Semester 09/10 / Solution
- Summer Semester 09 / Solution