Bending analysis of cantilever microbeams with three porosity distributions using physics-informed neural network and modified couple stress theory

Abstract

This study explores the use of a Physics-Informed Neural Network (PINN) framework to investigate the bending behavior of a cantilever microbeam made of porous material. PINN is a powerful approach that combines machine learning with physics principles to address the challenges of limited training data and enforce domain knowledge into the learning process, making them effective surrogate solvers for Partial Differential Equations (PDEs). In this work, a cantilever microbeam subjected to a uniformly distributed transverse load is examined, considering three different pore distributions including homogeneous, symmetric, and non-symmetric. The bending analysis incorporates the size effect by integrating the modified couple stress theory with the Euler-Bernoulli beam theory. First, the bending equation based on the modified couple stress theory is extended to include porous material properties. The governing equation is then solved using the Laplace transform. The PINN model is trained to approximate the solution by minimizing a loss function that accounts for residual errors at collocation points, as well as initial and boundary conditions. To enhance computational efficiency, the optimal hyperparameters of the PINN model are determined using a combination of Taguchi design of experiments and the Grey Relational Method. Taguchi-Grey approach effectively captures the trade-off between these objectives by normalizing and aggregating them into a single value to reflect the overall performance. The results are validated against analytical solutions based on Laplace transform, and the influence of key parameters such as microbeam length, length scale parameter, and porosity is systematically investigated.