Typically, there are two ways of considering load-time data in an FE-based fatigue analysis:
- The road load data is integrated in the FE analysis directly. The results in the form of transient stress responses serve as direct input for the subsequent fatigue analysis in TransMAX.
- The FE analysis uses a unit load case-based approach. The stresses are determined according to normalized static unit loads, the specific road load data are initially disregarded. The link with the road load data takes place in ChannelMAX applying the principle of linear superposition.
The first approach does not use the linear superposition principle, nonlinearities such as contact, large deformations can therefore be used in the FE analysis and the subsequent fatigue analysis.
Disadvantages of this procedure are above all to be found in the FE analysis and lie in the considerably high numerical effort, larger amounts of data as well as in the fact that in the non-linear case every road load data has to be recalculated. For these reasons, this procedure is usually limited to short & simple load profiles for reasons of efficiency.
The second option avoids all these disadvantages of the FE analysis and offers the advantages on the side of the fatigue analysis that general, random & almost arbitrarily long load-time profiles can be processed. Another significant advantage is that the FE results can be combined with various road load data in the fatigue analysis.
These advantages are bought by any compromises in accuracy due to the neglect of possible non-linearities.
The FEMFAT add-on tool Elastoloads bridges the gap between the two approaches, allows the use of non-linear FE calculation results without having to sacrifice the efficiency of a ChannelMAX analysis.
The core idea lies in an interpolation method, in which the FE analysis does not follow the original load history, but first calculates neighboring points.
These neighboring points result by placing a grid around the load curve. This results in a rectangular grid in the case of two forces and a cubic 3D grid for three forces. Non-linear FE analyzes are carried out for these discrete grid points. The deformation and stress states are interpolated from the results at the corner points for all times. Grid points that are not required for interpolation do not have to be calculated. This means that unnecessary states in the FE analysis and channels in ChannelMAX can be avoided.
Fig. 1: Discretization of Load Histories
The advantage of Elastoloads is that all the necessary input files for the FE solver or FEMFAT are created automatically. The expanded output options for post-processing in MetaPost are also particularly helpful, as the deformations, superposed stresses and damage can be animated in no time.
The application of a leaf spring is intended to illustrate the use of Elastoloads. As a special feature, a number of non-linearities supported by Elastoloads are included in this example (contact, hyper-elastic material behavior & large deformations).
Fig. 2: Leaf Spring Model
The external load is applied in the form of displacements in the x, y and z directions.
The load curve is discretized with five steps in the x-, eight in the y- and five in the z-direction (see figure above).
This results in a total of 25 FE analyzes with theoretically 200 FEMFAT channels. After filtering, 107 channels relevant for the given load histories remain.
The results show damage distributions and equivalent stress histories at selected points.
Fig. 3: Damage results & local stress histories
With Elastoloads it is possible to evaluate non-linear phenomena in combination with any length of road load data with an efficient channel-based approach in ChannelMAX with regard to durability. Due to the high degree of automation, this tool can be excellently included in the global simulation process.
A good selection of the level of discretion leads to a reduction in the required FE analyzes and a minimization of ChannelMAX channels.
Additional output in the form of a MetaPost session file simplifies the evaluation and enables even deeper insight into the underlying deformation and damage mechanisms.