OS-E: 2000 Introductory Example

Demonstrates how shape optimization can be used.


shapeopt1
Figure 1. Structural Model

Model Files

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

Model Description

For the cantilever beam, a shape is sought that minimizes the structural mass and allows a limited vertical deflection at the lower right corner.

The shape of the beam is defined using a linear combination of the two basis shapes below. The linear factors are the design variables in the optimization problem.

shapeopt2
Figure 2. Basis Shape 1

shapeopt3
Figure 3. Basis Shape 2

The basis shapes are defined using shape basis vectors. These can be generated using AutoDV, which is part of HyperMesh. The output file of AutoDV contains the definition of the DESVAR and DVGRID cards. This file can then be included in the OptiStruct input file, Bulk Data section, via the INCLUDE statement.

The optimization problem, objective and constraint functions, is defined in the same manner as the other types of structural optimization. OptiStruct then goes through an iteration process to solve the optimization problem.

Results

Figure 4 and Figure 5 show the optimization result of the cantilever beam.

shapeopt4
Figure 4. Final Shape

shapeopt5
Figure 5. Final Shape, Deformed with von Mises Stresses