Is minimizing mass identical to minimizing volume in OptiStruct?

Both formulations are identical as long as the same density r is used for all materials in the model. When minimizing the volume, the density value in the material card does not have to be given.

If different densities r exist in the design and the non-design space, then the optimization result may be different for minimizing mass and minimizing volume.

In a case where the design mass and the non-design mass are almost identical, but the design volume is much smaller than the non-design volume (Vdesign << Vnon-design), minimizing mass will give better results.

On the other hand, when the design volume and the non-design volume are almost identical, but the design mass is much smaller than the non-design mass (rdesign << rnon-design), minimizing volume will yield better results.