Optimization of functionally graded plates under Thermo-elastic free vibration using nature-based algorithms

This article presents the parametric optimization of the free vibration characteristics of a functionally graded material (FGM) plate exposed to nonlinear thermal loading using the finite element method and nature-based algorithms. The one-dimensional (1D) Fourier heat conduction equation is used to calculate temperature distributions over the thickness of the plate. Using Lagrange’s equation, we get the dynamic equation of motion for the plate. An eight-noded iso-parametric plate element with five degrees of freedom per node is used in the finite element formulation based on first-order shear deformation theory. Rectangular plates have temperature-dependent material characteristics; the thickness of the plates is scaled using a straightforward power law distribution. Here, the investigation of the FGM plate is conducted with two different boundary conditions, such as simple support and fully clamped. Additionally, new hybrid optimization approaches, namely RSM-Composite Desirability Optimization (RSM-CDO), Whale Optimization Algorithm (WOA), Corrected Moth Search Optimization (CMSO), Lichtenberg Algorithm Optimization (LAO), Sunflower Optimization Algorithm (SFO), and Forensic-Based Investigation Algorithm (FBI), are utilised to determine the best optimal solution, and the obtained findings are validated using confirmatory tests. © The Author(s) 2023.