This example demonstrates how to use the equation utility to define cross-sectional properties in a size optimization.

The structure is a cantilever beam of a length of 55 modeled with five CBAR elements. The cross-section of the beam is a solid circle. In each element, the diameter of the section is the design variable. Hence, there are five design variables. The cross-sectional properties such as area, moment of inertia, and torsional constant are calculated using the explicit formulas for a circle. In terms of the DEQATN card, they appear as:

$AREA

DEQATN,111,A(D)=PI(1)*D**2/4

$MOMENT OF INERTIA

DEQATN,122,I(D)=PI(1)*D**4/64

$TORSIONAL CONSTANT

DEQATN,133,J(D)=PI(1)*D**4/32

Using these equations, DVPREL2 statements are used to assign each design variable to the respective PBAR property. The statements that assign the diameter of the first bar element to the cross-sectional area of that element look like:

DESVAR,1,Diam1,10,1,20,0.5

DVPREL2,11,PBAR,1,4,,,111

+,DESVAR,1

The optimization problem to be solved is the minimization of the tip displacement with a volume constraint of 4000. Convergence was achieved after four iterations.

The result is given in the following table.

The input file for this example can be found in <install_directory>/demos/hwsolvers/optistruct/bar.fem.