Nonlinear Bending Investigation of Porous FGM Beams Subjected to Thermal Loading

Abstract

This paper focuses on the nonlinear deflection behavior of functionally graded material (FGM) beams with porosities (porous FGM beams) under thermal loadings using the Ritz method. Both uniform and symmetric porosity distributions over the beam cross-section are examined. Material properties change smoothly through the beam thickness and are evaluated using the modified rule of mixtures. The nonlinear thermal field across the beam is obtained through the solution of the steady-state heat conduction equation. The nonlinear governing equations are formulated through the virtual work principle within the framework of the first-order shear deformation theory, incorporating the geometric nonlinearity. The Ritz method is used to discretize the equations, and the resulting nonlinear equation system is solved using a direct iterative procedure. Convergence characteristics are demonstrated, and the accuracy of the results is verified through comparison with ABAQUS finite element simulations. Furthermore, a detailed parametric investigation is conducted to evaluate the influence of the porosity parameter, porosity distribution types, temperature variation, volume fraction exponent, and boundary conditions on the linear/nonlinear responses of the beams subjected to thermal loading. The present study provides a theoretical basis for the analysis and design of porous FGM beams under thermal loading, contributing to the development of lightweight and material-efficient structures for sustainable infrastructure.