用物理约束神经网络精准预测锥壳失稳载荷，实现更可靠的工程设计。
A Physics-informed Neural Network Approach for Robust Buckling Load Prediction and Reliability-Based Design of Thin Truncated Conical Shells
- 融合力学理论与数据的物理信息神经网络，约束预测结果符合弹性屈曲理论。
- 在133组实验数据上，相比普通神经网络，误差更低且物理合理性更强。
- 可为高敏感性薄壁结构提供考虑不确定性的可靠设计方法，适合航空航天应用。
薄壁截头圆锥壳因高强度重量比和几何高效性，广泛应用于航空航天、海洋及轻量化基础设施。其轴向压缩下的抗失稳能力对几何偏差、制造公差、材料变异及非线性失稳极为敏感。传统设计依赖保守的折减系数（KDF），如NASA SP-8019推荐值，未显式考虑壳体几何、制造质量、数据不确定性或目标可靠性。本文提出一种物理信息神经网络（PiNN）框架，用于预测截头圆锥壳临界失稳载荷，并将其集成至可靠性设计（RBD）中。模型结合几何与材料描述符，以及基于壳体稳定性理论和局部降刚度法（LRSM）的力学特征。采用物理信息损失函数，惩罚超过理论弹性屈曲载荷的不合法预测。框架基于133组轴压下Mylar锥壳实验数据训练与评估。相比传统深度神经网络（DNN），PiNN显著提升预测精度，降低均方误差，增强物理一致性。训练后的PiNN用于计算可靠性指标，并校准满足指定可靠性水平的安全一致折减系数。结果表明，PiNN-RBD框架为缺陷敏感壳体结构提供了高效、不确定性感知的设计途径。
原文摘要 · Abstract (English)
Thin-walled truncated conical shells are widely used in aerospace, marine, offshore, and lightweight infrastructure systems due to their high strength-to-weight ratio and geometric efficiency. Their buckling resistance under axial compression, however, is highly sensitive to geometric imperfections, manufacturing tolerances, material variability, and nonlinear instability effects. Conventional design procedures rely on conservative knockdown factors (KDFs), such as those recommended in NASA SP-8019, which do not explicitly account for shell geometry, fabrication quality, data uncertainty, or target reliability. This study develops a physics-informed neural network (PiNN) framework for predicting critical buckling loads of thin truncated conical shells and integrates the trained surrogate within a reliability-based design (RBD) formulation. The model combines geometric and material descriptors with mechanics-informed features derived from shell stability theory and the localized reduced stiffness method (LRSM). A physics-informed loss function penalizes mechanically inadmissible predictions exceeding the theoretical elastic buckling load. The framework is trained and evaluated using 133 experimental Mylar conical shell tests under axial compression. Compared with a conventional deep neural network (DNN), the PiNN improves predictive accuracy, reduces mean absolute error, and enhances physical consistency. The trained PiNN is then used to evaluate reliability indices and calibrate safety-consistent KDFs for prescribed target reliability levels. Results demonstrate that the PiNN-RBD framework provides an efficient approach for uncertainty-aware design of imperfection-sensitive shell structures.
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