Pro/MECHANICA® - How It Works
Pro/MECHANICA Structure uses adaptive p-element technology whereas traditional finite element codes use non-adaptive h-element technology. With h-elements a linear or quadratic equation is usually used to describe the element's deformation shape function. This has several consequences
i) These elements cannot follow accurately curved geometry, and one can get a faceting effect in the FE model which is not present in the true geometry.
ii) In areas of high stress gradient it is difficult for such elements to give an accurate result, because they are incapable of giving sufficient internal stress variation to follow the true stress contour.
iii) Lots of small elements are required. The solution to these problems with traditional codes is to decrease element size and increase element density in troublesome areas. The problem with this approach is that it relies either on an experienced analyst predicting the location of stress concentrations and hence where increased element density will be required before the analysis, or for very small elements to be used everywhere (significantly increasing run times).
iv) Manual Convergence. The solution is for the analyst to conduct a convergence study by manually intervening and re-meshing the model with smaller elements where necessary and repeating the run, and doing this again until the results do not change. However this is very time consuming and there is not always time in a project to undertake these convergence studies.
With Pro/MECHANICA, the use of higher order polynomial equations overcomes these problems.
i) The underlying geometry can be followed more precisely by using a 3rd order polynomial geometry shape function, (hence they are also sometimes called Geometric Elements), eliminating faceting.
ii) The elements use a polynomial equation to describe their stress shape function, which can go up to 9th order. This means that they can follow high stress gradients very closely.
iii) Fewer, larger elements. A by-product of this is that typical Geometric Element meshes use larger elements than traditional codes, because fewer high order p-elements are needed to track the same stress profile than traditional low-order h-elements. It also means that a tetrahedral solid mesh in Pro/MECHANICA is likely to give more reliable results than a tetrahedral solid mesh in other codes, where often a brick mesh would be required.
iv) Automatic Convergence. In order to run efficiently the p-order is not set to 9 for every element. Instead an automated solution strategy is used whereby an initial run, or pass as it is termed in Pro/MECHANICA, is conducted with the p-orders set to a low value for speed of response, and then the p-orders are automatically raised to a higher level in areas of high stress gradient or where greater accuracy is required. This achieves the ideal combination of accuracy and efficiency, whilst being virtually operator-independent with regard to meshing technique.
There is a choice of solution strategies available.
i) Single-Pass Adaptive (SPA), where the stress discontinuity at the element boundaries in the initial pass (where p=3) is used to determine the final p-order requirement for each element, and a stress error is reported in the results. This is now the default type of convergence for most analyses due to its combination of speed and overall accuracy.
ii) Multi-Pass Adaptive (MPA), where a series of passes are conducted, comparing the results with the previous pass in each case in order to determine where a further increase in p-order may be required. This continues until a user-requested percentage convergence has been achieved. Although this format typically takes longer to run, it provides a convergence curve which can be useful for quality control purposes, and it can be set up to converge on local areas of interest, rather than global results.
iii) Quick Check, which just does a single pass with all elements set to p=3. This can be used just as it says as a Quick Check on a model prior to conducting an SPA or MPA analysis. It can also be useful for very large models which need to be run on a resource-limited computer system, if absolute accuracy is not of prime importance, particularly if the elements in important areas are quite small. In this case indicative results can be achieved by just running a Quick Check analysis, but care should be taken in interpreting the results.
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