Finite element method

In the Technical Mechanics II lecture, you soon realize that estimation formulas for elastic systems are limited to simple problems. Arbitrary two- and three-dimensional stress and distortion states can no longer be treated with the derived analytical considerations. The aim of the finite element lecture is the numerical treatment of problems of elastic structures. For this purpose, the basics of elastostatics are first repeated and their implementation in a numerical method, in which the entire structure is discretized, is discussed. Since the finite element method is one of the most widespread and most frequently used methods, the lecturer considers it to be one of the fundamental lectures. The aim is not to get to know a special program system, but to address the properties of a numerical method hidden behind the colorful pictures and to program them in the exercises themselves.
Based on this content, the aim of this lecture is to consider material nonlinearities in the numerical method for the simulation of components. First, material models of viscoelasticity, elastoplasticity and viscoplasticity are motivated in order to gain knowledge for modeling material properties. Based on this, we look at the integration of such material models in finite element programs and learn about the solution of large non-linear Algebro differential equation systems.