Geometrically nonlinear bending of FGM beams with porosities in thermal environment and subjected to time-dependent loads

Abstract This paper aims to investigate effects of the geometrical nonlinearity on the bending behavior of functionally graded material (FGM) beams with porosities under time-dependent loads. Symmetric porosity distributions, whether uniform or non-uniform, are taken into account in this study. Material properties vary continuously across the beams’ thickness and they are estimated by on the rule of mixtures. Nonlinear temperature elevation in the beams is obtained by solving the steady-state heat conduction equation. The derivation of the nonlinear governing equations is carried out through application of the virtual work principle. The governing equations are discretized using a polynomial-based Ritz method and subsequently solved via a direct iterative approach. The convergence is verified, and the accuracy of the study is validated through comparisons with previous works for specific cases. Effects of temperature change, porosity parameter, and porosity distribution models, power law index, and time-dependent load types on the nonlinear deflection of the beams are thoroughly analyzed. The findings from the study provide valuable insights for the research, design, and operation of FGM beams with porosities working in thermal environments and subjected time-dependent loads.