Analytical modelling of a multifunctional heterogeneous beam-bending analysis

Abstract

Pores have a crucial role in shaping the features of functionally graded materials. If the distribution of pores is permitted to gradually rise from the outside inwards towards the center, many more features can be incorporated. A shear shape function is used to analyze the bending response of a two-directional functionally graded porous beam (FGPB), which can be considered a multifunctional heterogeneous material while accounting for both even as well as uneven porosity distributions. The power law is adapted to modify the material properties of FGPB through out the length and thickness dimensions. The notion of virtual displacements is applied when establishing equilibrium equations in FGPB. The Navier method is applied to clamped-clamped, clamped-free boundary conditions and simply supported boundary conditions to offer solutions to FGPB. The proposed methodology is supported by the numerical results of functionally graded beams from earlier studies. The dimensionless deflections and stresses under study are affected by gradient exponents, porosities, and aspect ratios.