> > Example 4: Topology Design with Stress Constraints

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
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    