Topology Optimization of Thin-walled Three-dimensional Structures by Decomposition into Two-dimensional Subproblems

  • Büscher, Keno Jann (Karlsruhe Institute of Technology)
  • Oellerich, Jan (The University of Tokyo)

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Thin-walled bent structures are widely used in lightweight engineering applications due to their high stiffness-to-weight ratio, manufacturability, and potential for material savings. However, topology optimization of such structures is computationally demanding when treated as fully three-dimensional problems, particularly when design variants are required to be manufacturable as single-part components. In this contribution, a level set–based topology optimization framework based on [1] for thin-walled, folded three-dimensional structures is proposed. The central idea is to unfold the three-dimensional geometry into the plane, such that the structure can be represented as a set of coupled two-dimensional subdomains. Each subdomain is treated as a two-dimensional problem, allowing the optimization to be performed in a reduced-dimensional setting. Physical consistency of the reconstructed three-dimensional structure is ensured by introducing suitable compatibility conditions at the folding lines. These conditions enforce material continuity at corresponding locations of adjacent subdomains and account for the interaction forces arising at the interfaces. As a result, the subproblems are coupled through boundary conditions derived from the interface forces and kinematic constraints. Unlike conventional approaches that directly optimize the full three-dimensional structure, the proposed method performs the optimization on the unfolded two-dimensional representation and subsequently reconstructs the three-dimensional geometry. This leads to a significant reduction in computational complexity while retaining the essential mechanical behavior of the structure. The applicability and effectiveness of the proposed framework are demonstrated on benchmark problems, including minimum mean compliance optimization under volume constraints. The results indicate that the method provides an efficient and robust alternative for the topology optimization of thin-walled bent structures.