OS-E: 0805 Two-dimensional Michell-truss

The two-dimensional Michell-truss is an optimal topology structure generated under bending.

Model Files

Before you begin, copy the file(s) used in this example to your working directory.

Model Description

The design space for this problem consists of a rectangle with a single vertical load at the free end. A circular cut-out is constrained in all translational degrees-of-freedom on the inside free edge.

This is a compliance minimization problem with a material volume fraction constraint of 20%. CQUAD4 (4-noded isoparametric) elements are used in a design space defined by a rectangular region with an aspect ratio approximately equal to one quarter of the short edge located closer to the edge away from the load.

Subcase Section
The objective function (compliance) is a subcase dependent response, therefore the response reference is part of the subcase definition. The constraint (volume fraction) is a global response, therefore the reference is outside the subcase.
DESGLB = 2
$
SUBCASE 1
 SPC = 1
 LOAD = 2
 DESOBJ = 1
Bulk Data Section
The responses and constraints are defined in the Bulk Data section. Two responses are defined here, the compliance (which is referenced by the objective function), and the volume fraction, referenced by the constraint statement to put up an upper bound of 0.2 (20% of the design space volume). The constraint statement is then referenced as a global constraint in the subcase section.
BEGIN BULK
$
DRESP1,1,comp,COMP
DRESP1,2,volfrac,VOLFRAC
DCONSTR,2,2,,0.2
Figure 1. Finite Element Mesh of the Design Space for the Two-dimensional Michell-truss

michell1

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

Results

The optimization converges in 29 iterations. The results are requested in HyperMesh binary format and written to the file, michell.res. The shape of the solution at the final iteration is visualized by creating a contour plot of the density results at the 29th iteration in the HyperMesh Contour panel.
Figure 2. Contour Plot of Density Results for the Two-dimensional Michell-truss

michell2