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# About

About

The boundary functions define the minimum/maximum limit thicknesses at the center and at the edges between two consecutive surfaces.
Each boundary function "b_{i}" between surfaces "i" and "i+1" is specified by a minimum setpoint thickness "th_{Mini}" (cell **min. thickness**), a maximum setpoint thickness "th_{Maxi}" (cell **max. thickness **) and a weight "w_{bi}" (cell **weight**) . The value of this function is very close to "0" when the effective thickness is between "th_{Mini}" and "th_{Maxi}" . It increases significantly when this thickness decreases after passing below "th_{Mini}" or when it increases after passing above "th_{Max i}".

All boundary functions are considered as merit functions so the overall merit function is in fact:

"Φ = ∑ w_{i}^{2}×(f_{i}-f_{i0})^{2} + ∑w_{bj}^{2}×b_{j}^{2}".

The "f_{i}" are the merit functions specified in the "merit functions" table and the "f_{i0}" are the associated setpoints.

In this way, during an optimization, the variable parameters tending to minimize the global merit function are calculated so that the thicknesses at the center and at the edges between two surfaces remain within the limits imposed by the boundary functions.

If a boundary function "b_{i}" is not activated, it is still taken into account. in this case "th_{Mini} = 0" and "th_{Maxi} = 9999999999" (almost infinite).

If it is activated, the "th_{Mini}" and "th_{Maxi}" values entered by the user are then taken into account.