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<p>A novel two-stage mapping modeling approach is proposed to enhance the Independent, Continuous and Mapping (ICM) method for structural topology optimization, named as T-ICM. Unlike the single-stage nonlinear mapping in conventional ICM (S-ICM), T-ICM contains two stages: Firstly, a discrete optimization model is established through linear mapping, and corresponding constraint functions are constructed based on discrete variables. Secondly, a continuous optimization model is established to approximate the discrete model obtained in the first stage by applying nonlinear mapping. Meanwhile, the element topology variables are transformed from discrete to continuous, and the constraint functions are converted into expressions based on continuous variables. The T-ICM framework retains compatibility with the Sequential Dual Quadratic Programming (SDQP) solver used in ICM method. Validated through a volume minimization problem under displacement constraints, T-ICM demonstrates superior topological clarity compared to the original ICM. Beyond ICM, the proposed two-stage strategy can be generalized to other ground structure-based methods (e.g., variable density methods) to amplify nonlinearity in penalty functions, achieving clearer topologies.</p>

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Reconstruction of Structural Topology Optimization Mapping: A Novel Two-Stage Mapping Modeling and Solution Approach

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Xi-Rong Peng,
  • Yun-Kang Sui

摘要

A novel two-stage mapping modeling approach is proposed to enhance the Independent, Continuous and Mapping (ICM) method for structural topology optimization, named as T-ICM. Unlike the single-stage nonlinear mapping in conventional ICM (S-ICM), T-ICM contains two stages: Firstly, a discrete optimization model is established through linear mapping, and corresponding constraint functions are constructed based on discrete variables. Secondly, a continuous optimization model is established to approximate the discrete model obtained in the first stage by applying nonlinear mapping. Meanwhile, the element topology variables are transformed from discrete to continuous, and the constraint functions are converted into expressions based on continuous variables. The T-ICM framework retains compatibility with the Sequential Dual Quadratic Programming (SDQP) solver used in ICM method. Validated through a volume minimization problem under displacement constraints, T-ICM demonstrates superior topological clarity compared to the original ICM. Beyond ICM, the proposed two-stage strategy can be generalized to other ground structure-based methods (e.g., variable density methods) to amplify nonlinearity in penalty functions, achieving clearer topologies.