Overall Quality Value

The total quality value for an element (`TOTAL') is calculated by averaging the contributions from all of the tests that are both applicable and currently switched on for that element type. These contributions are normalised between 0 and 1, so that for each test an ideal element will receive a score of 1, a very bad element will receive 0 (for example a degenerate element will score 0 for ASPECT), an element with a value at the criterion (set by the user or default) will receive a score of 0.5 and elements whose value is twice or more as far from the ideal, as the criterion is from the ideal, will receive a score of 0. Values in between these will be interpolated. These contributions are then averaged using the weights currently applicable.

The relative importance of a test is dependant on many factors, like element type, loading, boundary conditions and the user's personal preferance. Because of this the `average' may be weighted, in favour of (or against) various test types, using the UTILITY SETUP QUALITY command.

The overall quality value for an element (TOTAL) is then:

$$\frac {\sum_{i=1}^{N} W_{i} \ast \Vert 1 - \frac{Difference_... ...{Tolerance_{i}} \Vert \ast \delta_{i}} {\sum_{i=1}^{N} W_{i} }$$

where

N is the number of Quality Tests applied

$$\Vert P_{i}^{observed} - P_{i}^{ideal} \Vert$$ Difference_i

$$2 \ast \Vert P_{i}^{ideal}-P_{i}^{criterion} \Vert$$ Tolerance_i

$$\delta_{i} Difference_{i} < Tolerance_{i}$$

P_i^observed is the distortion value calculated for the ith test

P_i^ideal is the ideal value for the ith test for that element type

W_i is the weight of that test.

If W_i is not explicitly set with the UTILITY SETUP QUALITY command a default value of 1/N will be used, where N is the number of tests applicable to that element type.

The first test to fail is indicated when tabulating or displaying failed elements. The `weight' value is also used to order the application of the tests and so control the layout of information.