# Simcenter 3D Solutions Multi-Objective Topology Optimization with SOL200

2024-08-06T06:51:04.000-0400
Simcenter Nastran Simcenter 3D

## Summary

Multi-Objective Topology Optimization in SOL200 can be achieved by the use of the command DRSPAN in each subcase and by making use of DEQATN command to combine the responses and assemble them in a single objective equation resembling the desired weighting factor.

## Details

First of all it is important to mention that the nature of Topology Optimization, and that includes SOL200, is that it is of single objective! The method presented below however combines responses of different types that are coming from different subcases and by making them a fraction of their initial value and combining them together in a single equation as a target to be optimized, a multi-objective optimization on weighting basis is achieved.

The steps are as follow:

1. Define the "DRSPAN" command in each/respective subcase in "Case Control User Defined Text":
DRSPAN will assign the DRESP1 response to a specific subcase. It refers to a SET number, which we will define later in the Case Control in the solution (step 2).
https://docs.sw.siemens.com/en-US/doc/289054037/PL20221116635232682.QRG/id509496

2. Define the SET number for the respective response in case control in the solution:

This references the actual DRESP1 number (the response from the subcase):

3. Define DRESP1, DRESP2 and their composition in "User Defined Text" in "Bulk Data" in the solution:

As a direct response from the calculation, the type of the respective DRESP1 response should be declared, e.g. DWEIGHT for design weight and CMPLNCE for compliance as shown above.

Using DRESP2 we define the user-defined response by formulating the composition of the DREP1s with the help of the equation command DEQATN. As an example a 50:50 (or actually 1:1) ratio between weight and compliance minimization is defined. The weight response will be divided by its initial value as well as the compliance response. This should result in more or less 1:1 ratio or weighting between these responses at the start und during the optimization process. The initial value of compliance as shown above serves only as an example. It is quite possible that the initial values will vary from one subcase to the next (if more subcases are desired depending on the conditions). These initial values should be calculated beforehand.

Below are links to our online documentation for each of these commands:

4. Define design objective by referencing the ID number of DRESP2 in the DESOBJ solution in Case Control:

DESOBJ:
https://docs.sw.siemens.com/en-US/doc/289054037/PL20221116635232682.QRG/id509671

SummaryDetails

### Associated Components

Other SOL101 SOL103 SOL105 SOL106 SOL107 SOL108 SOL109 SOL110 SOL111-SOL112 SOL144 SOL145 SOL146 SOL153 SOL159 SOL200 SOL401 SOL402 SOL414 SOL601-SOL701 Superelement