D3. Data processing
D3. Data processing
D.3.1 Stresses/Deformations or Internal forces
It is important to define what you are looking for before starting the calculations, and this depends on the type of study:
for structures modeled as beam elements, we will prefer processing internal forces,
for civil engineering buildings, the stress approach allows us to understand the overall behavior of the structure by identifying different zones. On the other hand, when the objective is to obtain reinforcement results (quantity or internal forces), it is necessary to process the internal forces and to carry out the corresponding calculations in a second step.
D.3.2 Values at nodes, Gauss point values or values at the center
See also A.2 What is a finite element?
Generally, the software calculates the values of stresses and strains at the Gauss points, whose position is defined in the software's finite element manual. It can then infer the value at the center of the element. It extrapolates to each node and, since a node is usually linked to several elements, it computes the average of the values obtained for each element.
In regular zones, and with a proper mesh such as shown in paragraph C.3, the values at the center, at the nodes, or the Gauss points are very close.
The issue arises close to the peaks, where it is necessary to reflect on the most representative values.
Types of values displayed
Most software calculates the stresses at the integration points (or Gauss points). But there are two ways to visualize them:
at the elements – This method consists of directly plotting the average value on each element; an average of the values calculated at the integration points of the element. The plotted stresses then present discontinuities, which are accentuated when the discretization is not well adapted to the zone of interest. The results displayed in the center of the elements are reliable.
or at the nodes - This second method consists of displaying the mean values at the nodes. For each node, the calculated value is the weighted average of the stresses from the selected elements adjacent to the node. This treatment, called smoothing (*), is intended to display a continuous field, which may seem more relevant.
Stress field - Principle of calculation of the displayed values
(*) Do not confuse this smoothing action with the smoothing described in paragraphs D.5 and D.6, which consists of computing average forces over a given length.
In the figure below, the stresses calculated at the integration points have been extrapolated to the nodes before averaging. This is what some software packages do by default.
We can illustrate it using the example of the Br wheel (Example D - Simple case: modeling of a Br wheel). The software used does not give access to the values at the Gauss points.
Mapping of transverse bending moments - values at the center of the slabs - overview (28.52kN.m/m is an extreme calculation value)
Values at node 3 - they are different depending on the finite element
Values at the center of the elements - Zoom
Each software documentation should provide information on how it displays the solicitations and the options available. By default, software can propose that the linear part of the result of the integration point is extrapolated to the node while the non-linear part (plastic deformation for example) is copied. And an option in the same software allows the linear and non-linear parts to be copied to the nodes.
We will see later in paragraph D.5 the important variations that can be linked to smoothing the results at the nodes or elements.
D.3.3 Stress Analysis - Identification of Sensitive Zones
To follow up on the above details, displaying the stresses at the elements allows better visualization of areas of high discontinuity. For steel structures, software usually display the equivalent Von Mises stress, which gives an idea about the zones of high stress and/or with a high-stress gradient. One can also display the internal energy of deformation of each element. In reinforced concrete structures, either the stresses are displayed, or the reinforcement mapping, which allows visualizing the highly stressed areas.