Lattice Sizing+

Lattice Sizing+ is an extended sizing optimization process at the end of the sizing optimization during the second phase of lattice optimization.

Lattice Sizing+ is activated when LATPRM,CLEAN,YES (default) or LATPRM,CLEAN,LESS is present in the model. The Beam Cleaning procedure occurs after sizing optimization at the end of the second optimization phase to penalize beams with very low radii (below LATPRM,MINRAD). The beams below MINRAD are pushed to 0 or 1 via an embedded Topology optimization. The minimum value of the radii or aspect ratio can be controlled using LATPRM, MINRAD and/or LATPRM, R2LRATIO in conjunction with LATPRM, CLEAN.

The embedded topology optimization consists of two additional phases at the end of the sizing optimization phase. The first additional phase involves adding the following penalty term to the objective. This is equivalent to adding a value equal to the objective at convergence of the sizing optimization to the objective.

p e n = (\sum_{i = 1}^{n_{D V}} p e n_{i}) \frac{o b j_{c}}{p e n_{c}}

$p e n = (\sum_{i = 1}^{n_{D V}} p e n_{i}) \frac{o b j_{c}}{p e n_{c}}$

Where,

$p e n$ $p e n$: Penalty term added to the objective
$p e n_{i}$ $p e n_{i}$: Penalty value associated with each sizing design variable
$o b j_{c}$ $o b j_{c}$: Objective value at the convergence of the previous sizing optimization phase
$p e n_{c}$ $p e n_{c}$: Value of the total penalty at the end of the previous sizing optimization phase

The penalty value for each design variable (beam radius) is calculated based on the chosen method on LATPRM,CLEAN. If YES is selected, then the Heaviside penalty function is used, and the Quadratic penalty function is used, if LESS is selected.

Figure 1. Heaviside Penalty Function for Lattice Sizing+ (LATPRM,CLEAN,YES)

Figure 2. Quadratic Penalty Function for Lattice Sizing+ (LATPRM,CLEAN,LESS)

The second additional phase involves adding a penalty of 1000 times the Objective.

The Lattice Sizing+ process allows the cleaning up of small beams without much loss in compliance when compared to the converged step of the sizing optimization. Since the cleaning process is now visible to the optimizer, there is no violation of constraints and performance drop is minimized.