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Node elimination process

To improve the efficiency of fatigue life evaluation of complex components under complicated multiaxial and non-proportional loading conditions, Specialist Durability features a unique damage-based node elimination technique.

The basic idea for the node elimination process is to use shorter load histories to detect regions that are not critical with respect to fatigue damage. The main drawback of most of the other methods in use is that there is no clear idea of how to connect damages calculated for the short load histories to the damage of the full load histories. However, this is essential in determining whether or not a local area may be critical.

Specialist Durability handles this problem by its unique rainflow projector-based filtering algorithm. The overall process of node elimination is outlined as follows:

1. Set the actual set of locations to the full structure.

2. Produce shortened load histories L1, L2...Ln.

3. For i = 1 to n:Run an analysis with load history Li on the actual set of locations.Delete all locations in the actual set that prove to be noncritical.

As mentioned previously, producing shortened load histories and proving nodes to be noncritical are challenging points.

Filtering load histories

For filtering load histories, the method of the Siemens RP-Filter is used. Damage-based data reduction methods and the methods of peak valley and hysteresis filtering are introduced for uniaxial load histories. These methods may also be applied to several load histories at one time.

To apply this procedure for multiple load histories, the filtering methods are applied to each load history and regions that may be deleted are marked. At the end, all marked regions in time that are common to every history are erased from all load histories.

This method may be applied not only to the load histories themselves but also to linear combinations of load histories. In this manner, phase information can be handled correctly. As an example, consider the situations described below.

Example 1

In-Phase Loading

Suppose we have chosen a filter size slightly larger than the loop size that would be produced by considering a portion of two time histories, L1 and L2 individually. If the histories were considered independently, then these portions of the time histories would be marked for deletion.

However, if these two segments were from time histories that act simultaneously on the structure, linear combinations of the time histories must also be considered because these load histories may interact with one another at certain locations on the structure. For example, the load history combination will result in loops that will be larger than the set filter width, and therefore these segments should not be marked for deletion.

Specialist Durability automatically searches for these critical linear combinations of load, and hence does not delete this section of the time history during the load history filtering process.

Example 2

Out-of-Phase Loading

Next, consider the two segments L1 and L2 of the two time histories that are shown in Example 2, and again using a filter width that would be just above the loop size created in segment L1 or L2 individually. Now when considering the linear combination of the segments, the result is such that neither the segments individually nor are the linear combinations critical (above the filter level). In this case, Specialist Durability would mark these segments for deletion, and they would be eliminated from the load histories.

Note:

Algorithms based on peak slicing (selecting only points in time where any channel has a peak) cannot account for this phasing information.

You may set the filter width for the Specialist Durability filtering processes. To be able to specify the filter width independently from the material in use, the following procedure is used to calculate the filter width.

Definition of the Filter Width

Referring to the figure, for a given filter width, x, the corresponding number of sustainable cycles N(x) is calculated as the log-linear interpolation of NE and Nmax:

Notice that the horizontal distance of the sloped portion of the SN-curve is normalized, and that the value of x varies between 1 and 0 from the left to the right, respectively.

The filter width S(x) is the corresponding vertical distance and is read from the SN-Curve.

Note:

In the strain-life approach, the synthetic stress-life curve is used to calculate the filter width. You may also choose negative filter widths (x is to the right of the endurance limit) or filter widths larger than 1 (x is to the left of x=1). In these cases, S(x) will then be calculated from an extension of the sloped portion of the SN-curves.

A large value of x corresponds to a large value of the filter (S(x)) and will result in small time histories. For the different filter runs, you may enter different filter widths in the simulation objects. Specialist Durability automatically puts them in the proper order.

Representative elements

In a real structure some combinations of loads dominate others. Hence it is important to choose those combinations that represent the structure best. In the following sketch the situation is simple, since all local stress histories are proportional.

Representative Elements: Uniaxial Case

In this case, the left most point (closer to the fixed end of the cantilevered beam) has the highest local stress history. Therefore, this point is used for the filtering process, since sections that lead to no damage at this point will not lead to damage elsewhere as well.

The idea for the much more complex and complicated case of non-proportional loading is nevertheless quite similar. We will sketch the idea on the case of two non-proportional loads still leading to local uniaxial stress histories.

Representative Elements: Multiple Loads

The load influence factors now are classified for the amount of influence the first load history has. This may be done by dividing:

All locations having a similar fraction are put into one bin. Each bin will therefore contain locations that have nearly proportional local stress histories. Hence we can proceed as in the first example and choose from each bin the location and its stress history for the filtering process that have the maximal local load, that is, the one where is maximal.

In the general case the procedure is very similar, but you have to check for the critical planes individually. Here it is just the problem to define the bins.

Although you can control the rainflow projection method, we generally do not recommend changing these values.

Since the number of bins that may occur within a structure increases exponentially with the number of applied load cases, Specialist Durability restricts the number of load history combinations to 250.

The elimination process

For the elimination process, the actual set of locations is analyzed using a given shortened load history set. At the end of the analysis there is a damage value for each of the locations. You may now choose between two elimination practices: automatic thresholding and absolute thresholding.

Automatic thresholding

The maximum damage for the actual analysis run of all the shortened time histories is searched for (dmax). From the filtering process we gain information about the maximum damage reduction due to shortening the load histories:

Note:

In the computation state box, the reciprocal of this value is displayed.

Using the simulation objects, you can set one or more elimination safety factors. Then the location x is eliminated if its damage for the shortened load history d(x) fulfills:

αmax s d(x) < dmax

If x is eliminated, the value αmax d(x) is written to the result file and the elimination run number may be written to the result file depending on the settings in the simulation objects.

The automatic thresholding is used if the Use Absolute Elimination check box is cleared in the Node Elimination dialog box.

Parameter	Unit	Preset to
Use Absolute Elimination	Boolean	Has to be FALSE
Elimination Safety Factor	1	100

Absolute thresholding

Instead of comparing to dmax, you may give an absolute elimination threshold (θabs) in the simulation objects.

In this case, the locations are eliminated if αmax s d(x) < θabs.

You can use the method if you are not clear about whether the locations of maximal calculated damage might be due to numerical problems in the finite element analysis (like locations near load applications) and you did not eliminate those locations using element sets.

Parameter	Unit	Preset To
Use Absolute Elimination	Boolean	Has to be TRUE
Absolute Elimination Threshold	1	0.001

To specify these parameters in Specialist Durability, use the Simulation Objects command to create a node elimination simulation object.

Learn more

Quasi-static superposition, modal superposition, and transient analysis

Multiaxial fatigue

Vibrational loads

Temperature-dependent materials for Durability calculations

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