Example 4: Topology Design with Stress Constraints

Use the model hook.prt for this example.

Description

This example demonstrates how to use stress constraints in topology optimization. Topology optimization with stress constraints is computationally expensive.

Highlighted features

Minimize Mass Fraction, Stress constraints, Mirror Symmetry fabrication constraint, weight factor for objectives

Optimization problem statement

The following optimization problem will be created and solved:

• Objectives:

◦ Minimize Mass Fraction, weight factor 1.0

◦ Minimize Strain Energy, weight factor 2.0

• Subject to:

◦ Von Mises Stress ≤ 65 MPa

In engineering design, while stress may be the main requirement, you will also typically want a part to have a reasonable stiffness. Therefore, optimization purely to minimize mass with respect to stress can lead to non-physical parts being developed. To accommodate this, it is recommended to define a combined objective of minimize mass fraction and minimize strain energy.

In this example, we assign a higher weight factor to the minimize strain energy objective. The purpose is to help get a more polarized topology density result.

Analysis

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

Mesh control

Maximum element size: 4 mm

Topology region

• References:

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

• Init. mass fraction: 0.5

With the given initial mass fraction, the design constraint at the initial cycle should not be violated too much.

• Fabrication constraints:

◦ Mirror symmetry about the YZ plane with respect to coordinate system CS0

◦ Minimum member size: 8 mm

◦ Spread fraction: 0.5

Design objectives

Two objectives are defined:

• Minimize Mass Fraction, weight factor 1.0

• Minimize Strain Energy, weight factor 2.0

Design constraints

The von Mises stress constraints are applied on the part, except on the volume region 1 and 2, where load and boundary conditions are applied. The reason these volumes are excluded is that typically some artificially high stresses might exist in those regions.

The upper bound for the stress constraint is 65 MPa

Optimization study

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

Advanced settings:

• 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