Example 10: Topology Design with Frequency Constraints

Use the model subwoofer_cover.prt for this example.

Description

This example demonstrates how to use topology optimization to design a light and stiff structure with modal analysis.

Highlighted features

Minimize Mass Fraction, Modal Frequency constraints, Symmetry fabrication constraint, Extrusion fabrication constraint

Optimization problem statement

The following optimization problem will be created and solved:

• Objective:

◦ Minimize Mass Fraction

• Subject to:

◦ First Modal Frequency > 200 Hz

◦ Second Modal Frequency > 200 Hz

Analysis

The example contains one analysis. The constraints are shown in the image below:

Analysis settings:

• Eigenvalue method: SMS

• Frequency search range: 0–1000

• Number of modes to find: 6

• Mode Tracking: No

Mesh control

Maximum element size: 8 mm

Topology region

• References:

The component, excluding volume region 1 and 2, as shown in the image below:

• Init. mass fraction: 0.5

When you use mass fraction as constraint, it is recommended to use the same constraint bound value as the initial mass fraction value.

• Fabrication constraints:

◦ Mirror Symmetry about the YZ plane of coordinate system WCS

◦ Mirror Symmetry about the XZ plane of coordinate system WCS

◦ Extrusion along Z axis of coordinate system WCS

◦ Minimum Member Size: 16 mm

◦ Spread Fraction: 0.5

Design objective

Minimize Mass Fraction

Design constraints

• First Modal Frequency > 200 Hz

• Second Modal Frequency > 200 Hz

The reason we constrain the first two modal frequencies is that they are symmetric modes with same frequency values. The maximum displacement in two modes is at different locations, and all those locations need to be reinforced.

Optimization study

The study refers to the defined topology region, design objectives, and constraints

Advanced settings:

• Change Max. Design Cycles to 30

• For analysis output files, only the first and last cycle are requested.

• Use default settings for all other analysis and design parameters.

Topology Result

• Topology density isosurface

• Topology element density

Geometry Reconstruction

• Tessellated model

• Solid model