Release 11.0 Documentation for ANSYS Workbench
In situations where no information is available, there is never just one right answer. Below are hints about which physical quantities are usually described in terms of which distribution functions. This information might help you with the particular physical quantity you have in mind. Also below is a list of which distribution functions are usually used for which kind of phenomena. Keep in mind that you might need to choose from multiple options.
If you are designing a prototype, you could assume that the actual dimensions of the manufactured parts would be somewhere within the manufacturing tolerances. In this case it is reasonable to use a uniform distribution, where the tolerance bounds provide the lower and upper limits of the distribution function.
If the manufacturing process generates a part that is outside the tolerance band, one of two things may happen: the part must either be fixed (reworked) or scrapped. These two cases are usually on opposite ends of the tolerance band. An example of this is drilling a hole. If the hole is outside the tolerance band, but it is too small, the hole can just be drilled larger (reworked). If, however, the hole is larger than the tolerance band, then the problem is either expensive or impossible to fix. In such a situation, the parameters of the manufacturing process are typically tuned to hit the tolerance band closer to the rework side, steering clear of the side where parts need to be scrapped. In this case, a Beta distribution is more appropriate.
Often a Gaussian distribution is used. The fact that the normal distribution has no bounds (it spans minus infinity to infinity), is theoretically a severe violation of the fact that geometrical extensions are described by finite positive numbers only. However, in practice, this lack of bounds is irrelevant if the standard deviation is very small compared to the value of the geometric extension, as is typically true for geometric tolerances.
Very often the scatter of material data is described by a Gaussian distribution.
In some cases the material strength of a part is governed by the "weakest-link theory." The "weakest-link theory" assumes that the entire part will fail whenever its weakest spot fails. For material properties where the "weakest-link" assumptions are valid, the Weibull distribution might be applicable.
For some cases, it is acceptable to use the scatter information from a similar material type. For example, if you know that a material type very similar to the one you are using has a certain material property with a Gaussian distribution and a standard deviation of ±5% around the measured mean value, then you can assume that for the material type you are using, you only know its mean value. In this case, you could consider using a Gaussian distribution with a standard deviation of ±5% around the given mean value.
For loads, you usually only have a nominal or average value. You could ask the person who provided the nominal value the following questions: Out of 1000 components operated under real life conditions, what is the lowest load value any one of the components sees? What is the most likely load value? That is, what is the value that most of these 1000 components are subject to? What is the highest load value any one component would be subject to? To be safe you should ask these questions not only of the person who provided the nominal value, but also to one or more experts who are familiar with how your products are operated under real-life conditions. From all the answers you get, you can then consolidate what the minimum, the most likely, and the maximum value probably is. As verification, compare this picture with the nominal value that you would use for a deterministic analysis. The nominal value should be close to the most likely value unless using a conservative assumption. If the nominal value includes a conservative assumption (is biased), then its value is probably close to the maximum value. Finally, you can use a triangular distribution using the minimum, most likely, and maximum values obtained.
You also have to distinguish if the load values are random fields or single random variables. If the load is different from node to node (element to element), then it is most appropriate to include the program calculating the load in the analysis file. If the load is described by one or very few constant values, then you can also consider performing a Six Sigma Analysis with the program calculating these load values. Again, you need to provide an interface to transfer input data to this program and get output data (the loads) back to ANSYS. If there is more than just one single load value generated by the program, then you should also check for potential correlations.