A New Higher-Order Finite Element for Static Analysis of Two-Directional Functionally Graded Porous Beams

A new higher-order finite element for the static analysis of two-directional functionally graded (2D FG) porous beams subjected to various boundary conditions based on parabolic shear deformation theory (PSDT) is presented. The main purpose of this study is to predict the deflections and stresses of...

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Bibliographic Details
Published in:Arabian journal for science and engineering (2011) 2023-10, Vol.48 (10), p.13303-13321
Main Authors: Turan, Muhittin, Adiyaman, Gokhan
Format: Article
Language:English
Subjects:
Boundary conditions
Distribution functions
Engineering
Finite element method
Functionally gradient materials
Humanities and Social Sciences
Mathematical analysis
multidisciplinary
Normal stress
Polynomials
Porosity
Research Article-Civil Engineering
Science
Shear deformation
Shear stress
Two dimensional analysis
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Summary:A new higher-order finite element for the static analysis of two-directional functionally graded (2D FG) porous beams subjected to various boundary conditions based on parabolic shear deformation theory (PSDT) is presented. The main purpose of this study is to predict the deflections and stresses of 2D FG porous and non-porous beams with the help of the proposed finite element. Since a higher-order finite element with a third order polynomial is used, the deflections and stresses can be accurately and rapidly obtained even for short beams. In addition, the new higher-order element is free of shear locking phenomenon without requiring any shear correction factors. Three types of distribution functions were used for porosity in this study. To the author's knowledge, the sinusoidal uneven distribution function (FGP-3) is presented for the first time. The governing equations are derived by Lagrange’s principle using a parabolic shear deformation theory that considers normal and shear deformations. According to a power-law rule, the material change in the beam volume in both directions is defined. The dimensionless maximum transverse deflections, normal stresses, and shear stresses are obtained for various boundary conditions, gradation exponents ( p x , p z ) in the x- and z- directions, porosity coefficient ( e ), porosity distribution (FGP-1, FGP-2, FGP-3), and the slenderness ( L/h ). This study's new higher-order finite element gives results compatible with the literature and it can be used to accurately find the deflections and stresses for the 2D FG non-porous or porous beams subjected to various boundary conditions.
ISSN:2193-567X
1319-8025
2191-4281
DOI:10.1007/s13369-023-07742-8