Mechanical problems for free-shape and topology optimization in Flux 2D

It is now possible in Flux 2D to describe a mechanical problem and account for mechanical responses and constraints in the context of structural optimization.

Introduction

New tools allowing the inclusion of mechanical responses and constraints in Free-shape and Topology optimization problems are now available in Flux 2023.1.

The consideration of mechanical responses and constraints improves the results yielded by an optimization problem when compared to the optimization of a device based solely on electromagnetic quantities. Indeed, limiting the mechanical stress to not exceed the yield stress of the material or enforcing a mechanical compliance requirement in the parts subjected to optimization lead to more realistic and attainable designs. The design issued from such an optimization is more likely to be manufacturable and to result impervious to mechanical failure.

To benefit from mechanical responses and constraints in an optimization problem in Flux 2D, the user must describe a Mechanical problem and append its definition to the main Optimization problem. The procedure is described in the following sections:

Steps for creating a Mechanical problem for structural optimization

The tools used to describe a Mechanical problem for optimization are accessible through the Solver → Optimization → Mechanical optimization branch of the Data tree, as shown in Figure 1



Figure 1. The tools for creating a Mechanical problem for optimization in the Flux 2D Data Tree (highlighted inside the red rectangle).
The steps for creating a Mechanical problem for optimization are the following:
  1. Define one or more Mechanical regions.
  2. Define one or more Mechanical boundary conditions
  3. Using the previously created Mechanical regions and Mechanical boundary conditions entities, create the Mechanical problem.

Steps 1 to 3 above are detailed in the next sections.

Important: Once the Mechanical problem has been created, it must be integrated to the description of an Optimization problem. The Optimization problem must also contain one or more Mechanical responses in its description to benefit from the Mechanical problem definition. The Constraints describing the Optimization problem may also derive from Mechanical responses under those circumstances.
Remember: Mechanical responses may be created by clicking the Responses node of the Data tree and by selecting the option Mechanical response in the Physical quantity to optimize drop-down menu. There are two subtypes available, namely:
  • Von Mises stress and
  • Compliance.
Consequently, limiting the Von Mises stress or maximizing the compliance are examples of attainable constraints or objectives in Optimization problems accounting for a Mechanical problem.

How to create a Mechanical region?

To create a Mechanical region, click the Mechanical regions node of the Data tree shown in Figure 1.



Figure 2. The New Mechanical region dialog box.

Then, in the New Mechanical region dialog box:

  • Provide a name for the Mechanical region;
  • Select the type of the Mechanical region in the drop-down menu. Two region types are available:
    • Material region and
    • Air region (only useful in the context of free-shape optimization).
  • In the case of a Material region, also provide the following Mechanical properties of the region:
    • the Young modulus (MPa),
    • the Poisson ratio and
    • its Mass density (kg/m3).
  • Finally, inform the geometrical faces that integrate the Mechanical region in the List of application faces.

How to create a set of Mechanical boundary conditions?

To create a set of Mechanical boundary conditions, click the Mechanical boundary conditions node of the Data tree shown in Figure 1.



Figure 3. The New Mechanical boundary conditions dialog box.

Then, in the New Mechanical boundary conditions dialog box:

  • Provide a name for the Mechanical constraint;
  • Select an option from the Mechanical boundary conditions drop-down menu representing the type of boundary condition. Two possibilities are available:
    • Constraint on degrees of freedom of nodes and
    • Constraint on node displacement.
  • In the case of a Constraint on degrees of freedom of nodes, the user must inform if the nodal degrees of freedom
    • Radial translation,
    • Angular translation and
    • Normal rotation
    are Fixed or Free (unconstrained), by selecting the desired option in the corresponding drop-down menus.
  • On the other hand, for a Constraint on node displacement, the user must provide explicit constraint values for:
    • the Radial displacement (mm),
    • the Angular displacement (mm) and for
    • the Rotation (deg).
  • Finally, select the mesh nodes that will be subjected to the constraint. Two Node selection modes are available:
    • Node selection by line: applies the mechanical constraint to the mesh nodes lying on geometrical lines. A List of lines must be provided as an input.
    • Direct node selection: applies the mechanical constraint to the nodes identified by their numbering in the mesh.

How to create a Mechanical problem ?

To create a Mechanical problem, click the Mechanical problem node of the Data tree shown in Figure 1.



Figure 4. The New Mechanical problem dialog box.

Then, in the New Mechanical problem dialog box:

  • Provide the Name of the problem;
  • Select the Mechanical problem type from the drop-down menu.
    Note: Only Mechanical problems of type Centrifugal load are available in Flux 2023.1. This kind of mechanical problem is well adapted for the description of a structural mechanics problem representing the rotation of a solid around an axis, as in the case of the rotor of an electrical machine. To fully describe a Mechanical problem of type Centrifugal load, provide the Rotation speed (rpm) of the rotating body represented by the Mechanical regions.
  • Inform which of the previously created Mechanical regions integrate the problem by filling the List of mechanical regions.
  • Similarly, inform which of the previously created Mechanical boundary conditions integrate the problem by filling the List of mechanical regions.
Remember: Once the Mechanical problem has been created, it must be integrated to the description of an Optimization problem. The Optimization problem must also contain one or more Mechanical responses in its description to benefit from the Mechanical problem definition. The Constraints describing the Optimization problem may also derive from Mechanical responses under those circumstances.

Example of application

Let's consider the Free-shape optimisation of the flux barriers in the rotor of the synchronous reluctance machine shown in Figure 5.



Figure 5. The synchronous reluctance machine subjected to free-shape optimization with mechanical constraints (a). A few constraints (symmetry and mechanical) of the mechanical problem are shown in (b).

The Mechanical problem created to constrain the Free-shape optimization uses two Mechanical regions, namely:

  • One Material region corresponding to the rotor, without the shaft, characterized by the following parameters:
    • Young modulus = 200,000 MPa;
    • Poisson ratio = 0.3;
    • Mass density = 7,650 kg/m3.
  • One Air region, corresponding to the flux barriers in the rotor.
Two Mechanical boundary conditions are also required to complete the Mechanical problem:
  • The mesh nodes lying at the interface between the shaft and the rotor are supposed static and constrained in the structural mechanics problem. This is achieved through a Constraint on degrees of freedom of nodes, with all three degrees of freedom set to Fixed, applied to the green dotted arc of circle in Figure 5b.
  • The mesh nodes lying on the periodical boundaries of the rotor are allowed to move radially only. This condition is also enforced with a Constraint on degrees of freedom of nodes (applied to the blue dotted lines in Figure 5b), with the Radial translation degree of freedom set to Free, and the others set to Fixed.

The Rotation speed for the Centrifugal load of the Mechanical problem was considered equal to 15,000 rpm, the maximum working speed of the machine. The other parameters characterizing the Optimization problem are given in Table 1.

Table 1. The design goal and the constraints for the free-shape optimization problem with mechanical constraints.
Objective or Constraint Response or Constraint type Definition
Objective Torque Ripple Minimize
Constraint Von Mises stress Lower than 260 MPa (i.e., 80% of the yield stress value of the electric steel M330_35A used in the rotor)
Constraint Volume Lower than 80% of the initial design volume
Constraint Average torque Larger than 11.9 N.m
Constraint Symmetry 45 degrees symmetry (i.e., with respect to the red dotted line shown in Figure 5b

Figure 6 shows a comparison between the initial design of the flux barriers (a) and the obtained results (b).



Figure 6. The initial geometry of the rotor (a) and the optimized geometry obtained through free-shape optimization with mechanical constraints (b).

Software requirements

The requirements for using this feature are similar to the ones described in the Topology optimization in Flux 2D chapter of this release note. For further details on the versions of OptiStruct and on how to configure Flux Supervisor, please refer to the Software requirements section of that chapter.

Current limitations

This new feature is made available in Flux 2023.1 in Beta mode. Consequently certain limitations still apply. The most important cases are listed below:
  • Unavailable in the following applications:
    • Steady State AC Magnetic;
    • Non-magnetic or coupled applications.
  • Free-shape optimization problems using the Remeshing strategy option With Remeshing are currently not compatible with Mechanical problems. To benefit from Mechanical constraints, responses and problems in Free-shape optimization, the Remeshing strategy option No remeshing is required.