Isogeometric topology optimization of thin plate structures using a reaction-diffusion-based level-set approach

  • Le, Toan Minh (HCM University of Technology (HCMUT))
  • Leonetti, Leonardo (University of Calabria)

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Thin plate structures are widely employed across various engineering sectors, including civil, aerospace, and defense engineering. Topology optimization (TOP) approaches have been extensively applied as an effective means of obtaining optimal design solutions for such structural components. From a mathematical perspective, their structural model is commonly based on Kirchhoff plate theory, resulting in a fourth-order partial differential equations (PDEs)-based problem and posing significant challenges for standard finite element method (FEM)-based TOP approaches. In line with global efforts to address this issue, this paper develops a novel TOP methodology that combines a robust isogeometric analysis (IGA) framework with a reaction–diffusion equation (RDE)-based level set method. This framework exploits not only the substantial advantages of IGA (e.g., precise geometric representation, higher-order continuity, and seamless integration with computer-aided design (CAD) systems), but also the merits of level set-based TOP (e.g., clear material boundary representation and the elimination of checkerboard patterns) [1]. Specifically, the same Non-Uniform Rational B-Splines (NURBS) basis functions are concurrently employed for geometry modeling, approximation of state variables governed by high-order PDEs, and parameterization of the level set function (LSF). In contrast to conventional schemes, the design variables, i.e., the coefficients of the NURBS-parameterized LSF, are updated by solving the RDE, thereby alleviating the numerical difficulties commonly associated with the Hamilton-Jacobi (HJ) equation. Several benchmark examples involving compliance minimization of thin plate designs under volume constraints are presented. The obtained results confirm the effectiveness of the proposed method, particularly its computational efficiency compared with the HJ-based level set method and the SIMP-based TOP approach. Future work will focus on a more comprehensive evaluation of the method’s performance and its extension to the topology optimization of Kirchhoff-Love shell structures [2] for broader engineering applications.