Bending analysis of two-directional functionally graded beams using trigonometric series functions

Turan, Muhittin

doi:10.1007/s00419-022-02152-y

Cited by 13 publications

(4 citation statements)

References 32 publications

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“…(1) Finite element solution with the FSDT (2) Analytical solution with the FSDT (3) Analytical solution with the HSDT (4) FEM with the HSDT (5) FEM with the three-dimensional beam theory In Figures 3, 4 The buckling analysis of the FG beam was performed according to the finite element with 5 nodes and 16 degrees of freedom, using the FEM according to the HSDT. The results obtained were verified with the literature.…”

Section: Resultsmentioning

confidence: 99%

“…They obtained the equations of motion with Lagrange formulations. 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.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

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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“…Sonlu eleman modelleri iki düğüm noktasına sahiptir. Turan (2022), birinci mertebeden kayma deformasyonlu kiriş teorisini kullanarak farklı sınır şartlarına sahip iki doğrultulu FD kirişlerin eğilme analizlerini Navier tipi çözüm yönetimiyle yapmıştır.…”

Section: Giriş Introductionunclassified

Yüksek mertebe sonlu eleman modeliyle fonksiyonel derecelendirilmiş kirişlerin serbest titreşim ve statik analizi

Turan

HACIOĞLU

2023

Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Bu çalışmada, fonksiyonel derecelendirilmiş (FD) kirişlerin yüksek mertebeden kayma deformasyonlu kiriş teorisine dayalı sonlu eleman yöntemiyle serbest titreşim ve statik analizleri incelenmiştir. Sonlu elemanlar yöntemi için 5 düğümlü ve 16 serbestlikli bir sonlu eleman önerilmiştir. FD kirişin malzeme özelliği kiriş kalınlığı boyunca belli bir kuvvet kuralı fonksiyona bağlı olarak değişmektedir. Lagrange eşitliği ile denge denklemleri türetilmiştir. Farklı kuvvet fonksiyonu üst indisine (p), farklı sınır şartlarına ve farklı narinliklere (L/h) göre FD kirişin boyutsuz doğal frekansları, boyutsuz yer değiştirmeleri, boyutsuz normal ve kayma gerilmeleri elde edilmiştir. Çalışmadan elde edilen sonuçlar literatür ile karşılaştırılmış ve önerilen sonlu elemanın FD kirişler için oldukça uyumlu sonuçlar verdiği görülmüştür.

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“…Navier's method based on the FSDT for bending analysis of 2D FG beams subjected to various sets of boundary conditions was presented Turan [15]. Karamanli and Vo [16] investigated the flexural behaviour of 2D FG microbeams subjected to uniformly distributed load with various boundary conditions 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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Bending analysis of two-directional functionally graded beams using trigonometric series functions

Cited by 13 publications

References 32 publications

Buckling Analysis of Functionally Graded Beams Using the Finite Element Method

Buckling Analysis of Functionally Graded Beams Using the Finite Element Method

Yüksek mertebe sonlu eleman modeliyle fonksiyonel derecelendirilmiş kirişlerin serbest titreşim ve statik analizi

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

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