# Internal Forces Diagram/Surface Stresses - Smoothing Options

### Technical Article

The deformations of the FE nodes are always the first result of an FE calculation. Based on these deformations and the stiffness of the elements, it is possible to calculate strains, internal forces, and stresses.

Figure 01 - Deformations as the First Result of an FEM Calculation

RFEM provides triangular or quadrangular FE elements for surfaces, which means that there are three or four deformations per FE element that can be recalculated with the stiffness of the FE element (for example in stresses). Since several FE elements usually have the same FE node, there are as many results on one FE node as elements are present. The question now is how these results are evaluated. In the Project Navigator - Display, you can find five different options for displaying the distribution of internal forces within the surface.

Figure 02 - Options for the Distribution of Internal Forces for Surfaces

#### Constant on Elements

This option averages all nodal values of an FE element and the entire FE element has always the same value (smoothed). Therefore, there is no distribution in the FE element as with the other options. This method is used in the program for the material "Isotropic Nonlinear Elastic 2D/3D" because the limit stress is determined in this way.

Figure 03 - Distribution of Internal Forces "Constant on Elements"

#### Non Continuous

This option displays the raw data. Like in the following options, a hyperbolic paraboloid is used for the distribution within the element. However, the FE nodal values are not averaged with adjacent elements. For this reason, the result often looks discontinuously/graduated. In fact, significant differences between FE elements indicate that a finer mesh is necessary for more accurate results.

Figure 04 - Distribution of Internal Forces "Non Continuous"

#### Continuous within Surfaces

This option is the default setting. The values of all FE elements adjacent to an FE node are averaged. You can easily see or calculate this averaging in one point when comparing to the type "Non Continuous". This type of smoothing can correspond to a distribution with a finer mesh and is therefore often used for the evaluation. However, since this is a smooth display, it is recommended to carry out an analysis with "Non Continuous" in critical areas.

Figure 05 - Distribution of Internal Forces "Continuous Within Surfaces" (Default Setting)

#### Continuous Total

This option extends "Continuous within Surfaces" by averaging at the edge of the surface to the next surface as well. This results in a continuous distribution in the entire model and not only within one surface. Of course, it is also important to perform another analysis with the type "Non Continuous" in critical areas.

Figure 06 - Distribution of Internal Forces "Continuous Total"

#### Continuously by groups

With the last option, you can decide to have a continuous distribution between some surfaces or not. You can define groups where the distribution is "Continuous Total" and all remaining surfaces are then automatically set to "Continuous within Surfaces".Figure 07 - Distribution of Internal Forces "Continuous by groups"

#### Summary

When selecting the distribution of internal forces/stresses on surfaces, you have to specify that the result closest to the calculation is displayed as "Non Continuous". This distribution also strongly demonstrates the discretization due to the FEM calculation. In reality, such a distribution will probably not occur; therefore the smoothing "Continuous within Surfaces" is preset, which creates a continuous distribution within surfaces by means of smoothing. Since this distribution is closer to a real result, but does not correspond to the actual results, it is recommended to always analyze critical areas such as singularities (for example, point-like load introduction or connecting point of several surfaces).

#### Keywords

FE mesh Smoothing Singularity Stress peak