How to create a topology optimization problem?

Introduction

In spite of their diverse underlying principles, free-shape optimization and topological optimization may be regarded as complementary techniques and belong to the same framework of structural optimization methods offered in Flux 2D.
Consequently, they share common tools for the description of an optimization problem, as shown in Figure 1. These are accessible through the Solver→Optimization branch of the Data tree.
Figure 1. The structural optimization tools available in the Flux 2D Data Tree (highlighted inside the red rectangle). These tools are used to describe both free-shape optimization (previously available in Flux) and topological optimization problems.
Remember: For further details concerning the creation and configuration of all the entities occurring in the previous steps, the user may refer to the illustrated documentation embedded in each dialog box. Additionally, the user may also refer to the existing user guide pages on Free-Shape optimization.
Remember: The topology optimization tools are made available in Beta mode. A more comprehensive discussion on their use will be available in the user guide in an upcoming Flux version.

Steps

Users that are familiar with the free-shape optimization tools in Flux 2D should not experience difficulties to create a topology optimization problem. The creation workflow is as follows:
  1. Launch Flux 2D in Beta mode or in Advanced mode. To select one of these user modes, before executing Flux 2D, click the Options button in Flux Supervisor. Then, in System, select User mode and set the desired option.
  2. Create a project representing a first design of the device to be optimized. The project must satisfy the following rules:
    • The project application must be either the Magneto Static or Transient Magnetic application.
    • The geometry must be meshed. Moreover, the mesh must be very refined.
      Note: the Macro MeshingForMechanicalOptim.PFM that helps users obtain a suitable mesh.
    • It must have a coherent physical description (verifiable through the Check Physics command).
    • The project must be ready to be solved, i.e., it must contain a fully defined Solving scenario.
  3. Then, proceed to create one or more Responses by clicking the corresponding node of the Data tree. Responses may be regarded as physical quantities (magnetic flux, torque, force, volume, etc.) used to describe to optimization goals or constraints in the optimization problem.
  4. Similarly, create one or more Constraints by clicking the corresponding node of the Data tree. Constraints may be physical or geometrical in nature and are required to fully define the optimization problem.
  5. Create a structural mechanics problem (which may be regarded as a complementary constraint) by clicking the following nodes of the Data tree:
    • Mechanical regions.
    • Mechanical boundary conditions.
    • Mechanical problem.
    Important: The possibility of describing a Mechanical problem to further constrain the structural optimization procedure itself is a new feature that was not available in previous Flux versions. It may also be used with free-shape optimization problems and not only with topology optimization. For a comprehensive discussion on this new feature, please refer to the following chapter of this release note: Mechanical problems for free-shape and topology optimization.
    Important: The description of a mechanical problem is not mandatory, but is highly advisable for obtaining more realistic, mechanically compliant and manufacturable shapes as a result.
  6. Click the Optimization problem node of the Data tree to describe the topology optimization problem. Flux asks for the type of optimization (Minimization or Maximization), for the optimization goals (one or more of the previously created Responses), for one or more of the available Constraints and for an optional Mechanical problem definition.
  7. Finally, configure the Optimization options:
    • In the General tab and
    • In the Topology optimization tab.