Lineare Elastizitätstheorie / Lineare Finite Elemente Methode (Linear Elasticity Theory / Linear Finite Element Method)
For the analysis of plane surface structures, tensors are introduced to describe the kinematics, the equilibrium and the constitution of elastic problems. Boundary value problems of linear elasticity theory are thus formulated and solved analytically. In parallel, the finite element method is discussed from the simplest case of the truss to the hybrid disk formulation and programmed by the students themselves under guidance. The reason for approximations within numerics are taught and strategies for improvement are suggested. Advantages of computer-aided calculation lead to more advanced applications such as automated structural design. A focus of the course content is on the load-bearing action of sheaves.
Linear elasticity theory
- Basics of tensor calculation
- Kinematics of the deformable body
- Linearization of kinematics
- Stresses and equilibrium statements
- Constitution of linear elastic material
- Boundary value problems of linear elasticity theory
- Weak form and energy principle of linear elasticity theory
- Analytical solution for disks
- Polar coordinates for rotationally symmetric problems
Linear finite element method
- FEM for the truss, the expansion bar and the slice
- Boundary value problems and weak form solutions
- Choice and effect of the approach space for the approximation of the solution
- Main stress trajectories and truss analogy to control the FEM
- Notes on modeling and calculation using FEM
- Static condensation
- Mixed methods
- Hybrid stress/strain approach for the slice
FEM: presentation of theory + practical programming in MatLab (VBA or Fortran)
Lecture notes will be made available in the Moodle workroom BMSD-LSM.
The course is intended for students of the bachelor program Bauingenieurwesen (Civil Engineering) in the 5th semester.