An efficient curved beam element for thermo-mechanical nonlinear analysis of functionally graded porous beams

Rezaiee‐Pajand, Mohammad; Rajabzadeh-Safaei, Niloofar; Masoodi, Amir R.

doi:10.1016/j.istruc.2020.08.038

Cited by 32 publications

(8 citation statements)

References 51 publications

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“…Substituting Equations ( 9) and (10) into Equations ( 11) and ( 12), the resultant forces can be expressed including the material variation through the beam thickness.…”

Section: The Mathematical Formulation For Fgm Beam Analysismentioning

confidence: 99%

“…The beam material properties were assumed to be temperature-dependent and vary through-thickness. The exact free vibration and buckling analysis of tapered beam-column made of FGM material and assumed the P-FGM material variation along with the cross-section's height and the vibration behavior of composite coupled conical shell structures were presented in [9][10][11]. FGM beam bending solution for Timoshenko beams compared with those of Euler-Bernoulli beams is also presented in [12].…”

Section: Introductionmentioning

confidence: 99%

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A Simplified Stress Analysis of Functionally Graded Beams and Influence of Material Function on Deflection

Althoey

Ali

2021

Applied Sciences

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This paper aims at providing a simplified analytical solution for functionally graded beam stress analysis and optimized material gradation on the beam deflection. The power-law (P-FGM) and exponential (E-FGM) material functions were considered for an exact solution of the normal and shear stress distributions across the beam thickness. Optimization of material function on the FGM beam deflection, which is new of its kind, was also investigated considering both simply supported and cantilever beams. It was observed that the non-dimensional normal stress and shear stress are independent of the elastic moduli values of the constituent materials but rather depends on both the ratio of the elastic moduli and the location across the beam thickness in the E-FGM material function model. This observation was first validated from available kinds of literature and through numerical simulation using ABAQUS and extended to the P-FGM stress analysis. The maximum deflection on the FGM beam occurred for a homogenous steel beam while the minimum deflection was observed on the beam with a P-FGM material function. The results of this work demonstrate that if properly designed and optimized, FGMs can provide an alternative material solution in structural applications.

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“…Substituting Equations ( 9) and (10) into Equations ( 11) and ( 12), the resultant forces can be expressed including the material variation through the beam thickness.…”

Section: The Mathematical Formulation For Fgm Beam Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Simplified Stress Analysis of Functionally Graded Beams and Influence of Material Function on Deflection

Althoey

Ali

2021

Applied Sciences

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“…The elastic modulus of the beam varies continuously in the axial direction of the beam, according to a power-law model. sandwich beams incorporating Functionally Graded Materials (FGM) were investigated by Rezaiee-Pajand et al [16]; moreover, the investigation was done using two methods: (1) the Ritz method and the principle of minimum total potential energy based on the Timoshenko and Reddy beam theories to evaluate the bending of beams with varying cross sections and a four-node isoparametric beam element was developed by them to analyse porous beams through FGM in [17]. According to the conducted literature review, the majority of previous studies have either considered homogeneous beam properties or axially functionally graded beams or have adopted an analytical approach for FG tapered beams, and there is no antecedent study on the static analysis of these types of structures using transversal gradation of material Simple incremental approach for analysing optimal non-prismatic functionally graded beams…”

Section: Introductionmentioning

confidence: 99%

Simple Incremental Approach for Analysing Optimal Non-Prismatic Functionally Graded Beams

Ziou¹,

Guenfoud²

2023

ACAE

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This paper presents a simple incremental approach of analysing the static behaviour of functionally graded tapered beams. This approach involves dividing the non-uniform beam into segments with uniform cross-sections, and using two separate finite element models to analyse the structural behavior of slender beams (Euler-Bernoulli model) and deep beams (Timoshenko beam theory). The material properties of the beam vary according to a power law distribution through the thickness, resulting in smooth variations in the mechanical properties. The finite element system of equations is obtained using the principle of virtual work. Detailed information on the shape functions and stiffness matrix of the beam is provided, and the numerical results are evaluated and validated using data from the literature. The comparison demonstrates that the response of the functionally graded tapered beams is accurately assessed by the proposed approach. Additionally, the effects of material distribution, boundary conditions, and tapering parameter on the deflection behavior are presented. Results show that an increase in the power law index increases the flexibility of the functionally graded tapered beams, resulting in higher deflection. Furthermore, lower tapering parameters also result in higher deflection. Compared to other boundary conditions, clamped-clamped boundary conditions demonstrate the best performance in terms of maximum deflection.

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“…In recent years, functionally graded structures have been used in many modern engineering applications due to varying material properties over dimensions which allow them to improve the strength of material, high resistance to temperature shocks and high strength to weight ratio. Authors [1][2][3][4][5][6][7][8][9][10][11][12] devoted a considerable number of studies to predicting and to understanding the mechanics of functionally graded structures. In [1], the main idea of this paper's developed method was the control over the produced gradient and did not require burning binder phase.…”

Section: Introductionmentioning

confidence: 99%

Mechanical Behavior of 2D FGP Beam with Uneven Porosity Distribution

Hoang That Ton

2023

jaer

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An efficient curved beam element for thermo-mechanical nonlinear analysis of functionally graded porous beams

Cited by 32 publications

References 51 publications

A Simplified Stress Analysis of Functionally Graded Beams and Influence of Material Function on Deflection

A Simplified Stress Analysis of Functionally Graded Beams and Influence of Material Function on Deflection

Simple Incremental Approach for Analysing Optimal Non-Prismatic Functionally Graded Beams

Mechanical Behavior of 2D FGP Beam with Uneven Porosity Distribution

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