The air conditioner bracket is an optimal topology structure generated under both linear static stiffness and modal frequency response. Shell elements are used to ensure that the bracket is manufacturable using a casting process.

A concentrated mass, M, is used to model the air conditioner unit connected to the mounting bolts by beam elements. Shell elements close to the mounting bolt and engine bolt connections (shown as darker elements) are moved to a nondesign component. The model is constrained at two engine mounting bolts that are fixed for all displacements and rotations except for the rotation perpendicular to the plane of the bracket. The belt tension load is applied at the node representing the air conditioner bracket.

Subcase Section

Since the objective function (weighted combination of compliance and frequencies) is a global response, the response reference is outside of the subcase definition. The constraint (volume fraction) is a global response too, therefore the reference is outside the subcase. The weight factors are defined within the load cases.

DESOBJ = 1

DESGLB = 2

$

SUBCASE       1

 SPC    =    1

 LOAD   =    2

$

 WEIGHT =  1.0

$

SUBCASE       2

 SPC    =    2

 METHOD =    2

$

 MODEWEIGHT 1 1.0

 MODEWEIGHT 2 1.0

 MODEWEIGHT 3 1.0

$

 NORM = 40000.0

 

Bulk Data Section

The responses and constraints are defined in the bulk data section. Two responses are defined here, the weighted combination of compliance and reciprocal frequencies (referenced by the objective function), and the volume fraction, which is referenced by the constraint statement to put up an upper bound of 0.3 (30% of the design space volume). The constraint statement is then referenced as a global constraint in the subcase section.

BEGIN BULK

$

DRESP1,1,freqstat,COMB

DRESP1,2,volfrac,VOLFRAC

DCONSTR,2,2,,0.3

The same problem definition can also be achieved by using the equation utility DEQATN to define the weighted combination.

Finite element model of air conditioner bracket.

The OptiStruct output for the initial iteration appears as follows:

 

ITERATION   0
 

Subcase  Weight      Compliance                               Weight*Comp.

  1     1.000E+00         2.573592E+01                             2.573592E+01

                                                           ----------------

Sum of Weight*Compliance                                      2.573592E+01

 

Subcase   Mode        Weight     Frequency      Eigenvalue    Weight/Eigen

  2         1      1.000E+00   3.129449E+00   3.866299E+02   2.586453E-03

  2         2      1.000E+00   4.035579E+01   6.429414E+04   1.555352E-05

  2         3      1.000E+00   8.710232E+01   2.995154E+05   3.338726E-06

  2         4      0.000E+00   1.203149E+02   5.714770E+05   0.000000E+00

  2         5      0.000E+00   1.513964E+02   9.048794E+05   0.000000E+00

                                              -----------------

 

(Sum of Weight/Eigenvalue) / Sum of Weights       8.684483E-04

Mode Normalization Factor                         x  4.000E+04

                                              -----------------

Eigenvalue total weight                           3.473793E+01

Compliance total weight                           2.573592E+01

                                              -----------------

Objective Function                                6.047386E+01

 

Execution

This example is analyzed in the one-file setup with the file, acbrack.fem. The OptiStruct batch job is submitted using the command shell script, % optistruct acbrack.

Results

The optimization converges after 22 iterations. The results are requested in HyperMesh binary format and written to the file, acbrack.res. The shape of the solution at the final iteration is visualized by creating an assign plot of the density results at the 22nd iteration in the HyperMesh contour panel.

Density plot of air conditioner bracket for combined eigenvalue and compliance objective.

Two thick ribs extend from the engine bolts to the lower air conditioner attachment and one thin rib extends from the middle of the upper main rib to the upper air conditioner attachment. There is webbing between the two main ribs and a wide, half-height rib running through the upper half of the design space.

Many elements did not converge to either 100% dense or 0% dense. These elements can be forced toward 0% and 100% by increasing the discreteness parameter. This solution is acceptable because webbings and half-height ribs are manufacturable within a casting process.

Optimized models for linear static and frequency are analyzed separately.

The two main ribs from the combined solution are present in both solutions although they vary in thickness between the cases. The third rib, which is full height in the combined load case, appears only in the static solution and is thinner in the combined solution. The webbing between the two main ribs appears as several discrete crossribs in both separate solutions. The upper rib is half-height in the combined solution and appears in both the static and eigenvalue solutions. This rib is in a different position in each analysis. The thicker half-height rib in the combined solution is a compromise between the two.

Density plot for linear static load only.

Density plot for eigenvalue subcase only.

For the input file sample, see <install_directory>/demos/hwsolvers/optistruct/acbrack.fem.

See Also:

Example Problems