# What are the finite element steps

## Finite element method

### From ESOCAETWIKIPLUS

engl: finite element method Category: Level 1 theory

General information on this can be found, for example, at wikipedia: Finite Element Method

### simulation

The finite element method (FEM) is a simulation method in which small areas of a component or a calculation area - the finite elements - are used as a basis to map the physical behavior of the component.

The finite element method provides that the component to be calculated is divided into finite elements - i.e. small finite areas. This is the discretization.

For each of these elements - that is, for each small finite area - simply structured approach functions are selected and used that appropriately map the physical behavior. The elements are "finite", in contrast to infinitesimal calculus. The finite element method achieves an approximate solution of the differential equation by using the difference quotients instead of the differential quotients and evaluating them numerically. There are different types of elements, depending on which physics are to be simulated or which shape has been selected for the simulation model.

The relationship between neighboring elements results in a system of equations that has to be solved during the simulation.

The use of finite elements (the finite element method, FEM) includes after the idealization

In most cases, a technical statement is then made in the assessment based on the results.

### Self study

You will find a few sequences of images for self-study: 6 pages, 30..60 min
What is the Finite element method? The differential equation is set up for a mechanical bending beam. The solution will be

• theoretically as a closed solution,
• with a numerical approach and
• with the Finite element method outlined.

In comparison, you will see the essential principles and advantages of FEM. 17 pages, 60..90 min
Here an FEM application with numbers is followed in detail. For a structural mechanics component,

Then the finite element method is applied, with all working steps

can be followed in detail with numerical values. In comparison with the analytical solution, the possibilities and limits of the FEM become apparent. 7 pages, 15..30 min
From the theory (see also the simple example mentioned above) and everyday use of the Finite element method the conclusions presented here can be drawn. These "statements" are used to compile the essential properties of the FEM. They are predominantly applicable in everyday technical life and can mostly be used to plan a calculation. However, some remarks are made here to indicate restrictions.