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

Devasmit Dutta; Budhaditya De; Rohan Majumder; Sudip Kumar Mishra

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

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 $\rho$ using LRSM and Z

Feature type	Feature	Range / description
Original	Semi-vertex angle, $\beta$	$10^{\circ}$ – $60^{\circ}$
Original	Slant length, $L$	35.52–366.77 mm
Original	Base radius, $R$	99.73–169.17 mm
Original	Thickness, $t$	0.05–0.25 mm
Original	Young’s modulus, $E$	4826 MPa
Original	Poisson’s ratio, $\nu$	0.30–0.33

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
Model	$\mathbf{R^{2}}$	RMSE (N)	MAE (N)	95% CI Coverage
DNN	0.9916	16.81	9.64	0.991
PiNN	0.9925	15.74	9.32	0.996
Test Set
Model	$\mathbf{R^{2}}$	RMSE (N)	MAE (N)	95% CI Coverage
DNN	0.906	44.76	17.47	0.926

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 $N_{pred}$ 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: $N_{pred}/N_{exp}$ 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 $\gamma$ 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 ( $\gamma_{T}$ ) for $\frac{R_{a}}{t}=480$ , $\frac{L}{R_{a}}=1$ and 15% CoVs in $R_{a}$ and t.

Structural Mechanics

Structural mechanics studies how structures deform, carry loads, vibrate, buckle, and fail under different materials, geometries, and conditions.

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A Hybrid Gaussian Process-Extreme Gradient Boosting Machine Learning Framework for Robust Knockdown Factor Prediction and Reliability-Based Design of Thin Spherical Shell Caps

Budhaditya De, Rohan Majumder, Devasmit Dutta, Aman Deep Gupta+1

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

Structural Mechanics

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Elastic buckling remains a critical concern in the design of deep spherical shell caps, given that experiments reveal a significant reduction of critical loads from those predicted by linearized eigen-buckling analysis. This discrepancy has been attributed to initial geometric imperfections and is often reconciled through a dimensionless parameter, namely the knockdown factor (KDF). However, conventional KDFs (NASA SP-8007; Eurocode 3) are highly conservative, as they represent the lower bound of an extensive body of experimental data. This study aims to narrow the conservatism in the KDFs for spherical shell caps through machine learning (ML) regression models trained on experimental data on spherical shell buckling. A hybrid model is proposed by combining Gaussian Process Regression (GPR) with Extreme Gradient Boosting (XGBoost), and its improved performance is demonstrated over conventional ML algorithms, i.e., the Artificial Neural Network (ANN), Support Vector Regressor (SVR), Random Forest Regressor (RFR), and Histogram-based Gradient Boosting (HGBoost). Each of these models uses six input features and a single output, i.e., the KDF. The most critical feature affecting the KDF is ascertained through a sensitivity analysis. The study concludes with a reliability-based design framework that relies on the predictive ML model to obtain safety-consistent, yet less conservative, KDFs.

Abstract

Structural Mechanics

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