Elastostatic analysis of two-directional functionally graded beams using various beam theories and Symmetric Smoothed Particle Hydrodynamics method

Karamanlı, Armağan

doi:10.1016/j.compstruct.2016.10.065

Cited by 49 publications

(19 citation statements)

References 74 publications

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“…Seven components of Eq. (8) for 1D case are written as Details of the SSPH method can be found in [30,[42][43][44][45].…”

Section: Formulation Of Symmetricmentioning

confidence: 99%

“…Meshless methods are widely used in static and dynamic analyses of the isotropic, laminated composite and FGM beam problems [32][33][34][35][36][37][38]. However, the studies are very limited regarding to the analysis of two directional FG structures by employing a meshless method [26,30,[39][40][41]. The main novelty of this paper is that the flexure behavior of the two directional FGBs is analyzed based on a quasi-3D theory by using the SSPH method with four different end conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The main novelty of this paper is that the flexure behavior of the two directional FGBs is analyzed based on a quasi-3D theory by using the SSPH method with four different end conditions. Moreover, the weight (kernel) functions used for the numerical computations by employing the SSPH method given in [30,[42][43][44][45] cannot provide satisfactory results for the solution of these complex engineering problems. To overcome this deficiency, a weight function [46] which is used for the interpolation by employing the compactly supported radial basis function is introduced.…”

Section: Introductionmentioning

confidence: 99%

“…The buckling of Timoshenko beams composed of two directional FGM is studied in [29]. The static behavior of the two directional FGBs by using various beam theories is presented in [30]. The flexure of the two directional FG sandwich beams is analyzed in [31].…”

Section: Introductionmentioning

confidence: 99%

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Bending Analysis of Two Directional Functionally Graded Beams Using A Four-Unknown Shear and Normal Deformation Theory

Karamanlı¹

2018

Journal of Polytechnic

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The bending behaviour of two-directional functionally graded beams (FGBs) subjected to various sets of boundary conditions is investigated by using a shear and normal deformation theory and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. A simply supported conventional FGB problem is studied to validate the developed code. The comparison studies are performed along with the analytical solutions and the results from previous studies. The numerical calculations in terms of maximum dimensionless transverse deflections, dimensionless axial and transverse shear stresses are performed for various gradation exponents, aspect ratios (L/h) and sets of boundary conditions. The effects of the gradation exponents on the accuracy and the robustness of the SSPH method are also investigated for the two directional functionally graded beams which are having clamped-free boundary condition..

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“…Seven components of Eq. (8) for 1D case are written as Details of the SSPH method can be found in [30,[42][43][44][45].…”

Section: Formulation Of Symmetricmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bending Analysis of Two Directional Functionally Graded Beams Using A Four-Unknown Shear and Normal Deformation Theory

Karamanlı¹

2018

Journal of Polytechnic

Self Cite

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“…The dynamic characteristics of the bi-directional functionally graded beams were presented by using the Timoshenko beam formulation in [37]. The static behaviour of two directional FG beams was studied by using a meshless method in [38]. Morever, the studies for the static, dynamic c 2017 BISKA Bilisim Technology and buckling analysis of the FG sandwich structures are also very limited [39][40][41][42][43][44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Static behaviour of two-directional functionally graded sandwich beams using various beam theories

Karamanlı¹

2017

ntmsci

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This paper presents the static behaviour of two-directional functionally graded sandwich beams by using the Euler-Bernoulli, Timoshenko and Reddy-Bickford beam theories and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The SSPH code developed based on the present formulation of the functionally graded sandwich beam is validated by solving a simply supported conventional functionally graded beam problem. Numerical results which are in terms of maximum dimensionless transverse deflections, dimensionless axial and transverse shear stresses are compared with the analytical solutions and the results from previous studies. Various FG sandwich beam structures are investigated by considering different beam theories, aspect ratios (L/h) and sets of boundary conditions and using power-law distribution.

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A new modified Bessel‐type radial basis function for meshless methods: Utilized in the analysis of free vibration in 2D functionally graded Euler–Bernoulli beams

Hosseini,

Abbaspour,

Nazari

2024

Int J Numerical Modelling

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Radial basis functions (RBFs) are extensively employed in mesh‐free methods owing to their distinct properties. This study presents a novel RBF formulation based on a modified first‐kind Bessel function, introduced for the first time. The efficacy and precision of the proposed function are assessed through an examination of the free vibrations of Euler–Bernoulli beams composed of two‐directional functionally graded materials. Longitudinal and thickness property variations are modeled in polynomial and exponential forms, respectively. The performance of the novel RBF is scrutinized under various boundary conditions (clamped, simply supported, and free), and comparative analyses are conducted against similar investigations and an RBF based on the first‐kind Bessel function. Convergence analysis of the proposed modified first‐kind Bessel function‐based RBF reveals superior convergence rates compared to the first‐kind Bessel function‐based RBF. Moreover, a comparison between results obtained from modeling using the proposed RBF and exact solutions underscores the adequacy of this approach, with a maximum discrepancy of 4.933% observed under clamped‐free boundary conditions. In essence, the findings suggest that the proposed modified first‐kind Bessel function‐based RBF holds promise for analyzing the free vibrations of functionally graded Euler–Bernoulli beams. The primary aim of this research is to introduce and validate a new RBF based on a modified first‐kind Bessel function for the analysis of free vibrations in Euler–Bernoulli beams made of two‐directional functionally graded materials. The study focuses on evaluating the performance and accuracy of this novel RBF in comparison with existing RBFs and exact solutions. By addressing the limitations of conventional RBFs and proposing an innovative approach, this research aims to enhance the accuracy and efficiency of meshless methods in structural vibration analysis.

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Elastostatic analysis of two-directional functionally graded beams using various beam theories and Symmetric Smoothed Particle Hydrodynamics method

Cited by 49 publications

References 74 publications

Bending Analysis of Two Directional Functionally Graded Beams Using A Four-Unknown Shear and Normal Deformation Theory

Bending Analysis of Two Directional Functionally Graded Beams Using A Four-Unknown Shear and Normal Deformation Theory

Static behaviour of two-directional functionally graded sandwich beams using various beam theories

A new modified Bessel‐type radial basis function for meshless methods: Utilized in the analysis of free vibration in 2D functionally graded Euler–Bernoulli beams

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