Digital Teaching
moodle
Course Contents
Audience
Students of civil-engineering, mechanics, maths, physics
Contents
The lectures deal with finite-element methods for the numerical solution
of strongly nonlinear problems in the mechanics of solids and structures.
The nonlinearity may arise from geometrically or physically nonlinear behavior,
for the latter elastoplasticity is treated in depth. Furthermore, nonlinear
elastodynamics and non-steady heat conduction is considered.
Structure
0. basic elements of tensor algebra and tensor analysis
1. a primer in continuum mechanics:
- kinematics of finite deformations
- strain tensors and stress tensors
- balance laws
2. geometrical nonlinearity
- finite-element-formulation of 3D-beams and of plates
- bifurcation of equilibrium: linear/nonlinear stability analysis
(snap-through problems, buckling of rods and plates)
- Numerical Solution techniques: Newton-Raphson, path-following
algorithms
3. Inelastic material behaviour - as a case of material nonlinearity
- physical foundations of plastic deformation for crystalline solids
- constitutive equations for different elastoplasticity models
- Numerical solution procedures: time integration algorithms for
differential-algebraic equations, predictor-corrector-schemes,
linearization of constitutive equations, algorithmic tangent moduli
- damage
4. linear and nonlinear elastodynamics
5. non-steady heat-conduction
Exercices
Weekly computer-exercices applying a finite-element software (FEAP) bridge
the gap between theory and application to engineering problems.
A written elaboration of the weekly exercices is prerequisite for the oral examination.
examination
oral, 30 minutes
credit points: 6
Preconditions
"Finite Element Methods I"- knowledge is helpful
Online Offerings
moodle
- Lehrende: Dominik Schillinger