Multi-objective optimization of buckling load and natural frequency in functionally graded porous nanobeams using non-dominated sorting genetic Algorithm-II

This study investigates the fundamental natural frequency and critical buckling load of Functionally Graded Porous nanobeams supported by an elastic medium, addressing the need for optimized designs in advanced nanostructures. Utilizing a Genetic Algorithm and Non-Dominated Sorting Genetic Algorithm-II, the research aims to identify the Pareto front for these two objectives while incorporating surface effects. The nanobeam is modeled using Nonlocal Strain Gradient Theory and Gurtin-Murdoch surface elasticity theory, with governing equations solved via the Generalized Differential Quadrature Method based on Reddy's Third-order Shear Deformation Theory. Key input parameters, including temperature gradient, residual surface stress, porosity, and elastic foundation properties, are varied to train two Artificial Neural Networks for output prediction. Results indicate that for the fundamental frequency, significant factors include the material length scale and the Pasternak shear foundation parameter, while the critical buckling load is mainly influenced by the temperature gradient and the same material parameters. These findings provide critical insights for designers, allowing them to make informed decisions based on optimal values for eight input parameters.