Computer Aided Design

Part 4: The World of FEM

A short introduction to the world of the finite element method (FEM)

The FEM is an independent analytical method which may appear to have nothing to do with computer aided design at first. However, it should be a subject of our series because many intersections between CAD and FEM have resulted from innovations in IT. The FEM is, for example, now an integral part of many CAD programmes.

Although the basic principles of FEM were already developed decades ago, the method has only continued to develop strongly in recent years with increased computing power.

The finite element method (FEM) is a mathematical/mechanical approach to recognising physical problems in the geometry and structure of a component. The component is divided into a sufficiently large number of elements, but also sufficiently finely. This makes these elements finite and small, but they are still characterised by a finite number of parameters. These elements are dissolved piece by piece using software by means of differential equations. The results are ultimately presented in fringe plots which emphasise the hotspots of certain parameters.

The number of parameters which can be dissolved is dependent on the load configuration and material type. A designer will usually take the mechanical elongation, tension, reaction load and coarse deformation of the structure into account for a simple linear static analysis. There are, of course, many more parameters which have formed as a result of the increase in computing powers. These special methods also enable the designer to analyse problems with non-linear components. However, we will only illustrate components from the field of linear technology and the use of FEM for static loads.

The FEM is suitable for a quick verification of a component in the early design stage using CAD software. The analysis can also be used to analyse the structural tolerances of certain components.

We will present different cases of simple, linear structural analyses for which the FEM is extremely useful:

Complex geometric parts – The FEM is especially suitable for the analysis of basic geometric forms, e.g. the interplay between numerous features such as chamfers or holes. The method is also suitable for analysing geometric forms with numerous angles or curvatures.
Interaction of materials – The FEM is particularly suitable for the analysis of components or entire assemblies consisting of different materials. Conventional analytical structural methods are generally unsuitable if a non-isotropic material is involved. In most cases, these problems cannot be solved with conventional analytical methods. In contrast to the conventional analysis method, many special FEM tools can also be used to analyse and evaluate non-isotropic materials.
Problems due to inconsistent loads, e.g. caused by thermal and mechanical stresses – The FEM is the best way of checking inconsistent load profiles for load problems which do not fit precisely into the analytical profile fields. Every designer is presumably accustomed to the steel bending and expansion profiles in the technical handbooks. Although these lists are certainly impressive, they do not contain every possible load. Almost every FEM tool is also able to analyse different load types together in a relatively simple manner and summarise the results (e.g. pressure or inertia).
Non-linear analysis – Not all FEM tools can analyse the behaviour of non-linear components, but it can be argued that this is exactly where the FEM is essential. The numerical equations would be far too complex to tackle them with a pen and paper. More and more manufacturers are also using FEM tools for non-linear analyses, e.g. for dynamic impact analyses in the case of accident scenarios.

There is a lot more information on this issue, but this is a sound introduction for those who want to learn something about basic FE methods and how to make the most of them. As computing power has increased in recent decades, there are more and more kinds of technical problems which can be overcome with the FEM. It is, therefore, your task to immerse yourself in the world of FEM tools to establish how deep the FEM pool actually is!

In the fifth and last part of our series, we will discuss the use of high-performance research simulations.