Bending, vibration, buckling analysis of bi-directional FG porous microbeams with a variable material length scale parameter


Applied Mathematical Modelling, vol.91, pp.723-748, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 91
  • Publication Date: 2021
  • Doi Number: 10.1016/j.apm.2020.09.058
  • Journal Name: Applied Mathematical Modelling
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, Pollution Abstracts, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.723-748
  • Keywords: 2D FG porous microbeams, Bending, Buckling, Modified strain gradient theory, Vibration
  • Yıldız Technical University Affiliated: Yes


Finite elemen model for the structural behaviours of bi-directional (2D) FG porous microbeams based on a quasi-3D theory and the modified strain gradient theory (MSGT) is presented. As the main novelty of this study, in order to capture accurately the size effects, the MSGT is employed with three material length scale parameters (MLSPs) rather than the modifed couple stress theory (MCST) with only one MLSP. The material properties including three MLSPs are varied in both the axial and thickness directions as well as porosity. By using a quasi-3D theory, which inludes normal and shear deformations, the governing equations for static, vibration and buckling analysis are derived and solved by Hermite-cubic beam element for various boundary conditions. Through numerical examples, effects of variable MLSP and porosity as well as gradient index in two directions on the deflections, natural frequencies and buckling loads of 2D FG porous microbeams are examined.