Effect of (FG-CNT) Parabolic Distribution on Bending and Shear Deformation of (PMMA/CNT) Nano-Composite Porous Beams

The bending behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams with porosity was studied. The higher-order shear deformation beam theory (HSDT) was employed to determine the strain-displacement relationships, while a novel parabolic function was used to describe the carbon nanotube (CNT) volume fraction across the thickness. Four different porosity distribution coefficients were considered to evaluate their effects. The mechanical properties of FG-CNTRC are found using the rule of mixtures, which assumes that the single-walled carbon nanotubes (SWCNTs) are evenly distributed and lined up in a matrix of poly(methyl methacrylate) (PMMA). Governing equations were derived using Hamilton's principle and numerically solved. The influence of porosity, aspect ratio (L/d), CNT volume fraction (Vcnt), and the parabolic distribution on displacements and stresses were examined. The results highlight the significant impact of porosity on the bending performance of FG-CNTRC beams, and the parabolic CNT distribution plays a critical role in optimizing their mechanical response. This novel modeling approach provides valuable insights for the design and optimization of FG-CNTRC structures.