Search

This paper introduces the application of Physics-Informed Neural Network (PINN), a novel class of scientific machine learning techniques, for analyzing the static bending response of nanobeams as essential structural elements in micro/nanoelectromechanical systems, including nanoprobes, atomic force microscope sensors, nanoswitches, nanoactuators, and nanoscale biosensors on a three-parameter nonlinear elastic foundation. The study combines Euler–Bernoulli beam theory and Eringen’s nonlocal continuum theory to derive the governing differential equation using the minimum total potential energy principle. PINN is utilized for approximating the differential equation solution and identifying the nanobeam’s nonlocal parameter through an inverse problem with measurement data. The loss function incorporates terms representing the initial and boundary conditions, along with the differential equation residual at specific points in the domain and boundary. The research demonstrates PINN’s efficacy in analyzing nanobeam behavior on nonlinear elastic foundations, providing valuable insights into responses under different loading and boundary conditions. The proposed approach's accuracy and efficiency are validated through comparisons with existing literature. Additionally, the study investigates the effects of activation functions, collocation points’ number and distribution, nonlocal parameter, foundation stiffness coefficients, loading types, and various boundary conditions on nanobeam bending behavior.

In this article, peridynamic and finite strip sub-regions are coupled for the first time. Accordingly, in areas where non-local effects are important, the peridynamic theory is used, while in other areas, the finite strip method, which is an optimal method for solving plate problems, is applied. Static cases with and without crack are investigated using the coupling approach, and the results are compared with those available in the literature. A comprehensive parametric study is performed to investigate the effect of various parameters, such as grid size, the horizon value, the number of strips, and different term functions used in the finite strip. Finally, some examples involving non-uniform load conditions, plate with a hole and crack propagation are studied.

In this paper, a coupling of improved element-free Galerkin with the finite strip (IEFG-FS) is used to investigate the buckling analysis of cold-formed steel (CFS) channel-section beam with web holes. For this purpose, three sections of the CFS channel are considered under bending loading. These sections are divided into two sub-domains in which the IEFG method is used in sub-domain with openings, and the finite strip (FS) method is applied for another sub-domain. In the IEFG domain, the boundary conditions are enforced using the Lagrange multiplier method. In the following, hole size effects are investigated on the moment buckling load of sections. The results show that the IEFG-FS is an efficient method for buckling analysis of channel-section beams. Moreover, the presence of holes in CFS channel section reduces the moment buckling load, so that the decrease in the local buckling is more than the distortional and global buckling loads.