Abstract
This paper introduces a simple formulation for topology optimization problems ensuring manufacturability by machining. The method distinguishes itself from existing methods by using the advection–diffusion equation with Robin boundary conditions to perform a filtering of the design variables. Furthermore, the approach is easy to implement on unstructured meshes and in a distributed memory setting. Finally, the proposed approach can be performed with few to no continuation steps in any system parameters. Applications are demonstrated with topology optimization on unstructured meshes with up to 64 million elements and up to 29 milling tool directions.
Highlights
Topology optimization (TO) is a widely adopted method for structural optimization [1,2]
This paper presents an approach to perform the milling tool emulation, by solving the advection–diffusion equation with Robin boundary conditions
This paper is organized as follows; Section 2 introduces the formulation necessary for the advection–diffusion filtering step; Section 3 introduces the optimization problem used for numerical examples; Section 4 discusses the computational efficiency of the presented methodology; Section 5 presents two and three dimensional machinable results, with machining in one or multiple directions and Section 6 provides a discussion of the presented methodology and a conclusion
Summary
Topology optimization (TO) is a widely adopted method for structural optimization [1,2]. The freedom for TO to generate arbitrary topologies can result in structures with features, which are impossible to manufacture with traditional machining techniques This can be characterized as a mismatch between the constraints placed on the designer and the constraints used in the TO formulation. Gersborg and Andreasen [10] propose a method to consider an explicitly castable or millable design by using one design variable for each row or column of a structured grid This approach is contrasted by Guest and Zhu [11], which proposes a similar method, but retains all design variables and uses cumulative summation along rows or columns as a filter to ensure that a design can be cast or milled. This paper is organized as follows; Section 2 introduces the formulation necessary for the advection–diffusion filtering step; Section 3 introduces the optimization problem used for numerical examples; Section 4 discusses the computational efficiency of the presented methodology; Section 5 presents two and three dimensional machinable results, with machining in one or multiple directions and Section 6 provides a discussion of the presented methodology and a conclusion
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