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<p>This study presents an energy-based physics-informed neural network (PINN) framework for the static bending and free vibration analysis of laminated composite cylindrical panels. The formulation is established within a layerwise higher-order shear deformation theory (LW-HSDT), in which the layerwise kinematic description is incorporated into variational energy functionals. Static bending is solved by minimizing the total potential energy, while free vibration is formulated through a Rayleigh quotient. For higher-order vibration solutions, an additional mode-separation treatment is introduced to distinguish adjacent modes. The proposed framework is assessed through a series of benchmark examples, with particular attention to through thickness stress distributions, natural frequencies, and mode shapes. The predicted displacement, stress, and frequency results agree well with available three-dimensional elasticity solutions and advanced meshless results, demonstrating the capability of the proposed framework for the benchmark static bending and free vibration problems considered.</p>

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Energy-based PINNs with layerwise theory for static and free vibration of laminated cylindrical panels using Rayleigh quotient

  • 期刊论文

  • 发表日期：

    2026年7月14日

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  • Junan Tang,
  • Zhanjun Shao,
  • Yujie Cao,
  • Siyu Yi,
  • Baikuang Chen,
  • Fengqi Guo,
  • Zefeng Liu,
  • Ping Xiang

摘要

This study presents an energy-based physics-informed neural network (PINN) framework for the static bending and free vibration analysis of laminated composite cylindrical panels. The formulation is established within a layerwise higher-order shear deformation theory (LW-HSDT), in which the layerwise kinematic description is incorporated into variational energy functionals. Static bending is solved by minimizing the total potential energy, while free vibration is formulated through a Rayleigh quotient. For higher-order vibration solutions, an additional mode-separation treatment is introduced to distinguish adjacent modes. The proposed framework is assessed through a series of benchmark examples, with particular attention to through thickness stress distributions, natural frequencies, and mode shapes. The predicted displacement, stress, and frequency results agree well with available three-dimensional elasticity solutions and advanced meshless results, demonstrating the capability of the proposed framework for the benchmark static bending and free vibration problems considered.