cs.LGAug 22, 2026

A Physics-informed Neural Network Approach for Robust Buckling Load Prediction and Reliability-Based Design of Thin Truncated Conical Shells

Authors: Devasmit Dutta, Budhaditya De, Rohan Majumder, Sudip Kumar Mishra

Organizations: Department of Civil and Environmental Engineering, University of California Los Angeles, Los Angeles, CA, USA · Department of Civil and Infrastructure Engineering, Adani University, Ahmedabad, Gujarat, India · Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

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Abstract

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.

Figures & tables

Figure 1: Overview of the proposed physics-informed learning framework: (a) representative deep neural network architecture, (b) truncated conical shell geometry and coordinate definitions, and (c) PiNN workflow combining original features, physics-informed features, and physics-informed loss functions.
Figure 2: Power law regression fit between simulated ρ\rho using LRSM and Z
Feature typeFeatureRange / description
OriginalSemi-vertex angle, β\beta10∘10^{\circ} – 60∘60^{\circ}
OriginalSlant length, LL35.52–366.77 mm
OriginalBase radius, RR99.73–169.17 mm
OriginalThickness, tt0.05–0.25 mm
OriginalYoung’s modulus, EE4826 MPa
OriginalPoisson’s ratio, ν\nu0.30–0.33
Table 1: Original and physics-informed features used in the PiNN framework.
Figure 3: RMSE model loss history as function of epochs for baseline DNN and proposed PiNN models
Training Set
ModelR2\mathbf{R^{2}}RMSE (N)MAE (N)95% CI Coverage
DNN0.991616.819.640.991
PiNN0.992515.749.320.996
Test Set
ModelR2\mathbf{R^{2}}RMSE (N)MAE (N)95% CI Coverage
DNN0.90644.7617.470.926
Table 2: Comparison of predictive performance between the baseline DNN and the proposed PiNN for the training and test datasets.
Figure 4: Buckling load predictions NpredN_{pred} against the experimental values for the PiNN model and traditional DNN for training and test datasets. Plots (b) and (d) show enlarged views of plots (a) and (c) within the 0-90 N and 0-250 N range.
Figure 5: Npred/NexpN_{pred}/N_{exp} for the baseline DNN and PiNN models over the radius-to-thickness ratio R/t, with the dashed lines indicating the ±25% engineering acceptance band
Figure 6: PDPs for the four most influential features affecting buckling strength prediction of thin conical shells using baseline DNN and proposed PiNN models.
Figure 7: Geometric interpretation of the reliability index γ\gamma and the design point in standard normal space.
Figure 8: Contrasting PiNN-based and code/literature-based safety-consistent KDFs for varying target reliability indices ( γT\gamma_{T} ) for Rat=480\frac{R_{a}}{t}=480 , LRa=1\frac{L}{R_{a}}=1 and 15% CoVs in RaR_{a} and t.
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