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

Turan, Muhittin; Adıyaman, Gökhan

doi:10.1007/s13369-023-07742-8

Cited by 7 publications

(2 citation statements)

References 41 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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“…Ramteke and Panda [21] examined the free vibrations of a multi-directional FG structure considering the influences of variable grading and porosity distribution with HSDT. Turan and Adiyaman [22] used parabolic shear deformation theory to carry out static analysis on two-directional functionally graded (2D-FG) porous beams. Hung and Truong [23] investigated the free vibration response of sandwich beams with an FG porous core resting on a Winkler elastic foundation using various shear deformation theories.…”

Section: Introductionmentioning

confidence: 99%

A New Higher-Order Finite Element Model for Free Vibration and Buckling of Functionally Graded Sandwich Beams with Porous Core Resting on a Two-Parameter Elastic Foundation Using Quasi-3D Theory

Mohamed,

Kahya,

Şimşek

2024

Iran J Sci Technol Trans Civ Eng

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Bending analysis of functionally graded sandwich beams with general boundary conditions using a modified Fourier series method

Pu¹,

Jia²,

Luo³

et al. 2023

Arch Appl Mech

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

Cited by 7 publications

References 41 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

A New Higher-Order Finite Element Model for Free Vibration and Buckling of Functionally Graded Sandwich Beams with Porous Core Resting on a Two-Parameter Elastic Foundation Using Quasi-3D Theory

Bending analysis of functionally graded sandwich beams with general boundary conditions using a modified Fourier series method

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