Free Vibration and Buckling Analysis of Porous Two-Directional Functionally Graded Beams Using a Higher-Order Finite Element Model

Turan, Muhittin; Adıyaman, Gökhan

doi:10.1007/s42417-023-00898-5

Cited by 12 publications

(3 citation statements)

References 48 publications

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“…The novelty of this research lies in considering the influences of variable gradings, such as power-law, sigmoid, and exponential, as well as the effects of porosity distribution (even and uneven type). Turan and Adiyaman [16,17] presented a new higher-order finite element for the static, free vibration, and buckling analyses of 2D-FG porous beams under various boundary conditions. The method is based on the parabolic shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Mixed series solution for vibration and stability of porous bi-directional functionally graded beams

Turan

2024

Arch Appl Mech

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A new analytical solution based on the Ritz method is presented in this paper for analyzing the free vibration and buckling behavior of porous bi-directional functionally graded (2D-FG) beams under various boundary conditions. The solution is based on first-order shear deformation theory (FSDT). The selection of solution functions used in Ritz methods distinguishes the methods from each other and determines the accuracy of the analytical solution. To accurately capture the system's behavior and achieve the desired results, these functions have been carefully selected as a combination of polynomial and trigonometric expressions tailored as mixed series functions for each boundary condition. The study considers three types of porosity, namely PFG-1, PFG-2, and PFG-3. The equations of motion are derived using Lagrange's principle, taking into account the power-law variation of the beam material components throughout the volume. The non-dimensional fundamental frequencies and critical buckling loads are calculated for different boundary conditions, gradation exponents in the x and z directions (px, pz), slenderness (L/h), porosity coefficient (e), and porosity types. Initially, the accuracy of the mixed series functions is investigated for non-porous bi-directional functionally graded beams, and the numerical results are compared with existing literature to validate the proposed solution. Subsequently, the paper focuses on analyzing the influence of porosity on the free vibration and buckling behavior of bi-directional functionally graded beams using the developed solution method.

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Section: Introductionmentioning

confidence: 99%

Mixed series solution for vibration and stability of porous bi-directional functionally graded beams

Turan

2024

Arch Appl Mech

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“…[33] presented FE model for the structural behaviours of porous 2D microbeams based on a quasi-3D theory and the modified strain gradient theory (MSGT). Turan and Adiyaman presented a new higher-order finite element for the static [34] and free vibration [35] analysis of porous 2D FG beams subjected to various boundary conditions based on parabolic shear deformation theory (PSDT). The free vibration analysis of a porous 2D FG beams based on HSDT was investigated by Adiyaman [36] using FEM.…”

Section: Introductionmentioning

confidence: 99%

Bending and Buckling Analysis of Porous 2D Functionally Graded Beams with Exponential Material Property Variation

Adıyaman,

TURAN

2023

Preprint

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The bending and buckling analysis of porous two-directional (2D) functionally graded (FG) beams was conducted using a higher-order shear deformation theory (HSDT). The introduction of exponential functions to depict changes in material properties is a novel approach in the static analysis of 2D FG beams. Three distinct porosity distribution functions were taken into account. The governing equations were formulated through the application of Lagrange’s principle. During the numerical analysis, a finite element comprising two nodes and eight degrees of freedom (DOFs) was utilized. This choice facilitated accurate and efficient solutions, even for shorter beams, without the need for a shear correction factor. Notably, the obtained shear stresses aligned with actual values, registering as zero at both the top and bottom of the beam. The obtained results of the study were validated against findings reported in the literature. A parametric study was carried out to investigate the effects of porosity, porosity distributions, gradation parameters, slenderness, and boundary conditions on the non-dimensional deflections, stresses, critical buckling loads, and buckling mode shapes. It was found that both porosity and the distribution of porosity have noticeable effects on the static analysis of the beams.

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“…Turan [5] carried out bending analyses of two-directional FG beams using the FSDT, considering various boundary conditions according to the Navier method. Turan and Kahya [6] investigated the free vibration and buckling of FG sandwich beams with the Navier method under various boundary conditions. The displacement relations of the beam were obtained according to FSDT.…”

Section: Introductionmentioning

confidence: 99%

Buckling Analysis of Functionally Graded Beams Using the Finite Element Method

Turan

HACIOĞLU

2022

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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This study developed a finite element model according to higher-order shear deformation beam theory (HSDT) for the buckling analysis of functionally graded (FG) beams. Equilibrium equations of the FG beam are obtained from Lagrange’s equations. The beam element to be discussed within the scope of the study has 5 nodes and 16 degrees of freedom (DOF). As a result of the buckling analysis, the critical buckling load of the beam was obtained for various boundary conditions, power-law index (p), and slenderness (L/h). When the critical buckling loads obtained as a result of the analysis were compared with the literature, it was seen that they were quite compatible.

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Free Vibration and Buckling Analysis of Porous Two-Directional Functionally Graded Beams Using a Higher-Order Finite Element Model

Cited by 12 publications

References 48 publications

Mixed series solution for vibration and stability of porous bi-directional functionally graded beams

Mixed series solution for vibration and stability of porous bi-directional functionally graded beams

Bending and Buckling Analysis of Porous 2D Functionally Graded Beams with Exponential Material Property Variation

Buckling Analysis of Functionally Graded Beams Using the Finite Element Method

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