Risk-aware buckling design of functionally graded porous beams via machine-learning surrogates and reliability analysis

Satyasaibaba Pitta; Ranga Janardhana Ginka; Balakrishna Banavathu

doi:10.15282/ijame.23.1.2026.16.1014

Authors

Satyasaibaba Pitta Department of Mechanical Engineering, University College of Engineering, JNTUK, Kakinada-533003, India
Ranga Janardhana Ginka Department of Mechanical Engineering, Jawaharlal Nehru Technological University Anantapur, Anantapuramu-515002, India
Balakrishna Banavathu Department of Mechanical Engineering, University College of Engineering, JNTUK, Kakinada-533003, India

DOI:

https://doi.org/10.15282/ijame.23.1.2026.16.1014

Keywords:

Functionally graded porous beams, Buckling surrogate modelling, Reliability analysis, Conditional Value-at-Risk , Risk-aware structural design

Abstract

Functionally graded porous beams offer high stiffness-to-weight ratios, but their buckling strength is sensitive to induced porosity variability. Designers, therefore, need tools that are both fast and explicitly risk-aware. This study develops and validates an interpretable methodology that combines higher-order shear deformation theory, machine learning surrogates, and structural reliability analysis to support buckling design of functionally graded porous beams. Deterministic buckling responses are first generated using a higher-order shear deformation theory for two boundary conditions (simply supported and clamped-clamped), two slenderness ratios (L/h=10 and 40), geometric controls (taper and width), porosity indices 0<α<0.3, and two porosity patterns (Regular and Uneven). A gradient-boosted tree surrogate is then trained on the log-transformed dimensionless critical buckling load using five-fold cross-validation. Manufacturing variability in porosity is propagated through the surrogate via Monte Carlo simulation, and a companion First-order Reliability Method (FORM) in the porosity dimension provides efficient estimates of failure probability. Risk is summarized through domain-wise mean buckling capacity and Conditional Value-at-Risk (CVaR) at the 5% level (CVaR₅%), from which risk-return frontiers and “knee” designs distinguish risk-neutral from risk-averse choices. The surrogate generalizes strongly (out-of-fold log coefficient of determination, R²log=0.94; mean absolute error, MAE=2.7; mean absolute percentage error, MAPE=9.5%), while FORM tracks Monte Carlo with near-perfect concordance (average R²=0.9997; MAE(P_f)=0.0005; MAPE=0.33%), with small, interpretable deviations confined to slender, simply supported beams with uneven porosity. Across all regions, clamped-clamped, regular, and thick beams systematically dominate both mean and lower tail performance. Knee designs typically incur only 1-2% loss in mean capacity while retaining 95-99% of the best attainable CvaR, providing a reliable basis for compact, risk-aware buckling design guidance.

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