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<p>This paper presents a GPU-accelerated topology optimization (TO) framework based on Smoothed Particle Hydrodynamics (SPH) for lightweight thermoelastic design. The framework addresses coupled thermoelastic TO problems in which thermal performance and structural integrity are simultaneously optimized under mass constraints, with a particular focus on large-scale thermal devices where weight reduction is critical. Within a fixed-particle, density-based setting, this work establishes, to the best of our knowledge, the first steady-state SPH-based TO formulation for three-dimensional coupled thermoelastic problems with consistent discrete-adjoint sensitivities. Material properties, including Young’s modulus, thermal conductivity, and the thermal stress coefficient (TSC), are interpolated using the Rational Approximation of Material Properties (RAMP) scheme, and the resulting optimization problem is solved using the Method of Moving Asymptotes (MMA). To reduce the computational cost of particle-based analysis, the governing and adjoint equations are solved using a fully matrix-free Preconditioned Conjugate Gradient (PCG) solver implemented on GPUs. The local particle-interaction structure of SPH is exploited to evaluate the state and adjoint operators without explicitly assembling global sparse matrices. In addition, a lightweight on-the-fly reduced-order model (ROM) based on proper orthogonal decomposition (POD) is incorporated as an auxiliary initial-guess strategy to improve iterative solver convergence without modifying the governing equations or solver tolerances. The proposed framework is verified through three-dimensional structural and thermal benchmark problems, including an irregular fixed-particle compliance case with locally assigned representative volumes. Its large-scale feasibility is further demonstrated through coupled thermoelastic multi-objective design examples involving up to tens of millions of particles on a single GPU. The results show that the proposed framework can generate physically meaningful lightweight thermoelastic designs while enabling systematic exploration of thermal–structural trade-offs.</p>

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Multi-objective thermoelastic topology optimization using GPU-accelerated smoothed particle hydrodynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月31日

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  • Ju Hyeong Lee,
  • Eung Soo Kim,
  • Min Luo

摘要

This paper presents a GPU-accelerated topology optimization (TO) framework based on Smoothed Particle Hydrodynamics (SPH) for lightweight thermoelastic design. The framework addresses coupled thermoelastic TO problems in which thermal performance and structural integrity are simultaneously optimized under mass constraints, with a particular focus on large-scale thermal devices where weight reduction is critical. Within a fixed-particle, density-based setting, this work establishes, to the best of our knowledge, the first steady-state SPH-based TO formulation for three-dimensional coupled thermoelastic problems with consistent discrete-adjoint sensitivities. Material properties, including Young’s modulus, thermal conductivity, and the thermal stress coefficient (TSC), are interpolated using the Rational Approximation of Material Properties (RAMP) scheme, and the resulting optimization problem is solved using the Method of Moving Asymptotes (MMA). To reduce the computational cost of particle-based analysis, the governing and adjoint equations are solved using a fully matrix-free Preconditioned Conjugate Gradient (PCG) solver implemented on GPUs. The local particle-interaction structure of SPH is exploited to evaluate the state and adjoint operators without explicitly assembling global sparse matrices. In addition, a lightweight on-the-fly reduced-order model (ROM) based on proper orthogonal decomposition (POD) is incorporated as an auxiliary initial-guess strategy to improve iterative solver convergence without modifying the governing equations or solver tolerances. The proposed framework is verified through three-dimensional structural and thermal benchmark problems, including an irregular fixed-particle compliance case with locally assigned representative volumes. Its large-scale feasibility is further demonstrated through coupled thermoelastic multi-objective design examples involving up to tens of millions of particles on a single GPU. The results show that the proposed framework can generate physically meaningful lightweight thermoelastic designs while enabling systematic exploration of thermal–structural trade-offs.