# FEM-Simulation

## FEM-Simulation optimizes product development

The finite element method is a proven method to shorten the development time of new products. The method based on numerical analyses helps to manufacture durable and highly resilient products. This also ensures optimal operational safety.

### What is a FEM simulation?

A FEM simulation shows how a component or material reacts to certain influences. It is based on the finite element method (FEM). With this numerical calculation method, a component or an entire assembly is divided into a finite number of elements (sub-areas). This makes it possible to calculate the mechanical behavior of the individual sub-areas and ultimately that of the entire component. The FEM simulation is based on special algorithms that determine approximate values using a complex combination of differential equations. A powerful computer with high computing power is required for a FEM simulation. FEM software is often combined with CAD applications. The results of the FEM simulation can be used for a wide variety of areas with various physical issues. One of the most common applications is strength analysis on solid components with complex shapes. The finite element analysis is used for technical tasks in

- medical technology
- aerospace engineering
- construction
- vehicle construction
- mechanical and plant engineering
- consumer goods industry
- engineering

The procedure is therefore suitable to

- achieve results when no analytical calculation is possible
- compare several designs with each other
- understand the general behavior of a component or a system
- detect and correct critical points
- recognize and avoid oversizing
- find out the most critical influences on the behavior of the component
- examine components which are arithmetically difficult to test

A FEM simulation is worthwhile in terms of time and cost, especially when it comes to prototypes or products that are expensive to manufacture and would require a lot of effort to test. In particular, parts to be manufactured with lightweight construction benefit from the greater dynamics that can be achieved with FEM simulation, the reduced use of materials and optimized energy efficiency.

### What are singularities?

Singularities are critical points that arise due to discontinuities in the geometry, the material or the boundary conditions and which require special attention in the finite element model. At these points a strong mesh refinement is required to achieve reliable results. In structural mechanics, many local stress peaks often occur at these points, the value and extent of which can strongly depend on how finely the mesh is resolved. Singularities can have different causes:

- nooks (corner singularities)
- introduction of loads
- contact between different components
- combination of different materials

### Which FEM mesh is suitable for operational durability?

In order to determine the fatigue strength of a component, a high mesh quality is necessary. In order to represent the resulting stress precisely, the FEM mesh must be as fine as possible for the static or cyclical calculation. As a rule of thumb in structural mechanics: at least 5 to 6 square elements on an arc of 90 degrees. The component must also be finely networked in all three spatial directions for the service life calculation, because the voltage drop in the depth direction is also evaluated.

### What is the principle of the finite element method?

With the finite element method, the component to be analyzed is divided into many smaller parts with a simple two- or three-dimensional shape. Thanks to their simple geometric structure, the physical behavior of these finite elements can be easily calculated using special approach functions. The behavior of the entire component can be inferred from the reaction of these partial bodies to loads, forces and boundary conditions and from the radiation of the reactions and loads from one element to the other. In order to obtain an approximate value that is as precise as possible, ever more and ever smaller elements are used, but approach functions with ever higher value can also be used.

### Methods of FEM calculation

In order to be able to carry out calculations on the basis of the finite element method, the component geometry must first be read in from its CAD program. Then the required entries are made in the FEM preprocessor. Mesh parameters such as element type, element size, material properties, boundary conditions and loads acting on the component such as temperature or pressure are then entered. After the component has been subdivided into small elements, a sufficiently fine mesh is created. Special approach functions are defined for the elements that describe their behavior on influences and the boundary conditions. These are differential equations that describe the respective physical law. These differential equations, in combination with the respective boundary conditions, initial and transition conditions of all elements, result in a complete system of equations. This is then approximately solved using the equation solver implemented in the FEM simulation software. In mechanical analysis, the displacements (deformations) are a primary result quantity. Strain and tension values can be derived from this. The result based on the behavior of the partial bodies allows the reaction of the entire component to be predicted. Finally, the finite element analysis must be validated. The numerical method even allows combined physical tasks and is therefore a versatile tool. With its help, costly mistakes in real prototypes can be avoided in advance. In addition, the evaluation of the FEM simulation reduces the development time. The finite element method enables, among other things, calculations for:

- linear and non-linear statics
- thermomechanics
- dynamism
- forming simulation
- operational stability

### Possible sources of error

In general, the following errors can occur in the FEM simulation:

- An incorrect problem analysis can be carried out due to insufficient basic knowledge
- If the rules of FEM meshing are not observed, this would result in the approximate solution deviating more
- Elements with approach functions that are unsuitable for the problem are used
- Inadequate material parameters are used
- Acting loads are not taken into account or incorrectly assumed
- Other boundary conditions are not applied or are applied in a simplified way

In order to exclude possible errors, the simulation must be verified. This can be done, for example, by comparing a simulation and the results obtained in the test.

### Applications and structures

The finite element method is used for:

- Structural analyses. They are used to determine material and component loads and deformations as well as to analyze contacts.
- Stiffness analyses. Using these, the FEM engineer can determine the deformation of the component caused by pressure or tension.
- Strength calculations. These determine whether the respective component has a strength which, complies with the relevant standards.
- Life cycle analyses. They play a particularly important role in the development of new products. If components and entire assemblies are not sufficiently durable, product recalls will result in considerable costs.
- Creep calculations. With their help, the temperature and time-dependent plastic deformation of a material or component under load (creep behavior) can be determined.
- Thermal simulations. They illustrate the mechanical effect of heat on components. In the manufacture of solar modules, for example, while soldering the cells there can be thermally induced expansions and mechanical stresses, which are visualized with the help of the FEM simulation software.
- Vibration analyses. They are used to determine how the action of loads stimulates the natural frequencies of components: The construction can fail as a result of upswings.

### FEM simulation software

Software for performing FEM simulations is made up of different modules and is always structured in a similar way. It is chosen according to the focus of the application. Which software is the right one depends on the requirements of the respective company. Large companies often buy a complete CAE platform with many analysis functions, some interaction functions and other tools. Smaller companies prefer low-cost solutions or CAD simulations, which are usually limited to structural simulation.

### FEM simulation with optical measurement technology from GOM

The non-contact optical measurement technology from GOM offers efficient material testing in various scenarios. It can be easily integrated into existing test fixtures and examines the behavior of materials, components and fixtures in 2D or 3D. It does not matter whether the structures are rigid or flexible. Optical measurement systems from GOM test the effect of thermal and mechanical loads and offer a wide range of possible uses for the measurement results. Such measuring systems can be used

- to support numerical simulations by determining material parameters by determining boundary conditions
- to verify numerical simulations by comparing and verifying boundary conditions through full-surface comparison of results
- in material characterization
- in product development
- for quality assurance

The contactless optical measurement technology from GOM offers the possibility to test different sheet materials under the influence of the flow stress. When developing new forming tools, you have to decide on a design model. For this purpose, the behavior of the models under the influence of certain loads must be considered. It is immediately visible where the critical points are and corresponding corrections can be made.