Critical buckling load prediction in tapered axially functionally graded nanobeams using machine learning under different boundary conditions

This study presents a machine learning (ML) framework for predicting the critical buckling loads of tapered axially functionally graded (AFG) nanobeams resting on elastic foundations, governed by Eringen’s nonlocal elasticity theory. Due to their position-dependent stiffness and complex boundary conditions, closed-form solutions for such nanobeams are computationally expensive and analytically intractable. To address this, four supervised data-driven regression models are developed: linear regression (LR), polynomial regression (PR), support vector machine (SVM), and artificial neural network (ANN). These models are used to predict buckling loads for three boundary conditions: clamped–clamped (C–C), simply supported (S-S), and clamped-simply supported (C–S). A comprehensive dataset is generated using a finely discretized parametric sweep of the beam’s geometric and material properties. Pearson correlation coefficient (PCC) and variance inflation factor (VIF) analyses are conducted to ensure feature relevance and independence. Results show that the ANN model consistently outperform other test models, achieving coefficient of determination ( R 2 ) values exceeding 99%, root mean square error (RMSE) values below 1.1 (in normalized units), and mean absolute error (MAE) values below 0.67 (in normalized units) across all boundary conditions. The findings demonstrate that ML and ANN offer a robust and computationally efficient surrogate to traditional methods, with strong generalization capabilities.