Isogeometric analysis for bending, buckling and free vibration of multi-directional functionally graded porous plates with variable thickness

• Published in: European physical journal plus Vol. 137; no. 6; p. 694
• Main Authors: Mirzaei, Saeed, Hejazi, Mehrdad, Ansari, Reza
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2022; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; B spline functions; Basis functions; Behavior; Bending; Boundary conditions; Buckling; Complex Systems; Condensed Matter Physics; Deformation; Deformation effects; Equations of motion; Free vibration; Functionally gradient materials; Hamilton's principle; Investigations; Material properties; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Parameters; Physics; Physics and Astronomy; Porosity; Porous materials; Porous plates; Regular Article; Shear deformation; Shells; Theoretical; Variable thickness; Vibration; Vibration analysis
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-022-02902-5

In this paper, the isogeometric analysis based on the non-uniform rational B-spline (NURBS) basis functions is used to study of the bending, buckling and free vibration of the multi-directional functionally graded porous plates with variable thickness. The third-order shear deformation theory is used to account for shear deformation effect, which does not require any shear correction factors. The material properties of the plates are estimated by the rule of mixture and the Mori–Tanaka scheme. The C 1 required degree of continuity is easily obtained by increasing the order of the NURBS basis functions. The governing equations of motion are extracted by Hamilton’s principle and then discretised by the isogeometric analysis approach. The effect of different length-to-thickness ratios, material gradations, thickness variations, porosity parameters, and the different boundary conditions on the bending, buckling and free vibration of rectangular, circular and elliptical multi-directional functionally graded porous plates are evaluated. The effectiveness of the proposed method is verified by comparing its numerical results with those of other methods reported in the relevant literature. The presented results show that the variable thickness, porosity parameter and material gradations have a significant effect on the mechanical responses of the plates. Decreasing the thickness and increasing the porosity due to reducing the stiffness of the plate decrease the buckling load and frequencies and increase the deformation of the plate.