Efficient buckling prediction of strain gradient beams using a semi-analytical approach and artificial neural network

This study proposes an efficient and accurate computational framework for the buckling analysis of Euler–Bernoulli microbeams modeled using Strain Gradient Elasticity (SGE) theory. The sixth-order governing equations derived from SGE are solved via a combination of the Initial Value Method and an Approximate Transfer Matrix formulation based on a truncated matricant series. This semi-analytical approach eliminates symbolic computation and enables precise evaluation of dimensionless critical buckling loads under various classical boundary conditions. A feedforward Artificial Neural Network (ANN) is trained on computed buckling data corresponding to (Formula presented.) values ranging from 1/10 to 1/20 and tested on intermediate values not included in the training. The ANN model demonstrates highly accurate predictions for unseen (Formula presented.) values, exhibiting strong agreement with the analytical buckling results. This combined framework not only overcomes the symbolic complexity associated with high-order differential equations but also provides an efficient and generalizable predictive model for microscale structural stability analysis. The results reveal that increasing the gradient coefficient significantly raises the critical buckling load, reflecting the size-dependent stiffening behavior inherent in SGE theory. The proposed methodology effectively integrates analytical rigor with data-driven efficiency, representing a significant and novel contribution to microscale structural mechanics.