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# Single variate analysis method-stable warpage

To determine the part warpage attributable to each of these variates, three individual analyses are run where in each case the contribution of just one contributor is taken into account by eliminating the effect of the other two. Visual inspection of the magnitude of the part deflections in each single variate case indicates the dominant cause of warpage. This functionality is available for Midplane, Dual Domain and 3D analysis technologies.

## Differential Cooling Single Variate Analysis

This analysis calculates the shrinkage contribution due solely to differential cooling.

For the top and bottom of each element, and for the perpendicular and parallel directions, the differential cooling component of the shrinkage is determined by subtracting the differential shrinkage and orientation effects contributions from the total shrinkage determined from the shrinkage calculations as part of the Fill+Pack analysis.

For example, for the parallel orientation direction of the top of the element, the contribution from cooling would be,

where

• is the parallel shrinkage value from the packing analysis.
• is the difference between the temperature on the top of the element and room temperature.
• is the average of and
• is the linear shrinkage value, as defined for the differential shrinkage variate.

## Differential Shrinkage Single Variate Analysis

This analysis calculates the shrinkage contribution due solely to differential shrinkage.

The shrinkage contribution due to orientation effects is eliminated by assigning to each element the same shrinkage value in both the parallel and perpendicular material orientation directions. This value is the linear shrinkage value , given by:

where is the isotropic shrinkage determined in the shrinkage calculations as part of the Fill+Pack analysis.

The contribution of differential cooling is eliminated by assigning this value to both the top and the bottom of the element.

## Orientation Effects Single Variate Analysis

This analysis calculates the shrinkage contribution due solely to orientation effects.

The shrinkage contribution due to differential shrinkage is eliminated by subtracting the linear shrinkage value , from the parallel and perpendicular shrinkage results determined in the shrinkage calculations as part of the Fill+Pack analysis.

The shrinkage contribution due to differential cooling is eliminated by assigning the same parallel and perpendicular shrinkage value to both the top and the bottom of the element.