An elasticity solution for functionally graded thick-walled tube subjected to internal pressure

Xin, Libiao; Dui, Guansuo; Yang, Shengyou; Zhang, Jiamei

doi:10.1016/j.ijmecsci.2014.08.028

Cited by 49 publications

(16 citation statements)

References 15 publications

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“…Since the mechanical loads (inner and outer pressures) are systematically studied in [25], in what follows we solely seek the stresses and radial displacement induced by temperature change. As a consequence, for the sake of simplicity the inner and outer surfaces are assumed traction-free, namely σ r | r =a = 0 and σ r | r =b = 0.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Poisson's ratio that is assumed to be a constant v = v 1 = v 2 since the spatial variation in Poisson's ratio has less practical significance than in the other material properties and the assumption of the same Poisson's ratio supplies considerable mathematical simplification [31]. Our previous paper [25,26] analyzed the problem of different Poisson's ratios for the elastic problem of the FGM tube and the results showed that the effects of Poisson's ratio on the stresses are not obvious.…”

Section: Thermoelastic Problemmentioning

confidence: 99%

“…In most actual systems, the overall elastic modulus, the thermal expansion coefficient, the thermal conductivity, and the density of the FGM tube cannot be found directly, but they can be obtained in terms of their properties of constituents and the volume fractions in a certain regulation, which have been calculated and used in our previous papers [25,26].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Thermoelastic Analysis of a Functionally Graded Rotating Thick-Walled Tube Subjected to Mechanical and Thermal Loads

Xin

Yang

et al. 2015

Int J Thermophys

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A thermoelastic solution for the functionally graded rotating thick-walled tube subjected to axisymmetric mechanical and thermal loads is given in terms of volume fractions of constituents. We assume that the tube consists of two linear elastic constituents and the volume fraction of one phase is a power function varied in the radial direction. By using the assumption of a uniform strain field within the representative volume element, the theoretical solutions of the displacement and the stresses are presented. Based on the relation of the volume average stresses of constituents and the macroscopic stresses of the composite material in micromechanics, the present method can avoid the assumption of the distribution regularities of unknown overall material parameters appeared in existing papers, such as Young's modulus, thermal expansion coefficient, thermal conductivity, and density. The effects of the angular velocity, the volume fraction, the ratio of two thermal expansion coefficients, the ratio of two thermal conductivities, and the ratio of two densities on the displacement and stresses are systematically studied, which should help structural engineers and material scientists optimally design thick-walled tube comprised inhomogeneous materials.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Thermoelastic Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Thermoelastic Analysis of a Functionally Graded Rotating Thick-Walled Tube Subjected to Mechanical and Thermal Loads

Xin

Yang

et al. 2015

Int J Thermophys

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“…with C 3 and C 4 are integral constants. The function F is denote for the hypergeometric function based on equation (11) in [30] and the constants in For convenience, rewriting u r p ( ) as = + u r C P r C Q r 25…”

Section: Theoretical Analysismentioning

confidence: 99%

Revisiting the electroelastic solution for an FGPM thick-walled cylinder subjected to mechanical and electric loadings

Wang

Dui

Xin

2020

Mater. Res. Express

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Theoretical analysis for an empty thick-walled FGPM cylinder exposed to electric and mechanical loadings are investigated. The cylinder is a composite material composed of PZT4 and PVDF and the volume fraction of PZT4 is given by the power law with three controllable parameters which can cover more complex circumstances. The hypergeometric equation of the radial displacement is acquired by utilizing the Voigt method, and the solutions of the stresses and the electric potential are obtained after solving the radial displacement. The method in this paper is appropriate for real functionally graded piezoelectric materials and can avoid assumptions about unknown overall material parameters appeared in previous references. Finally, the impacts of the parameter n in volume fraction of FGPM cylinder on mechanical and electric behaviors are examined. Furthermore, the distinction between the hoop stress and radial stress is discussed to decrease the pressure concentration in FGPM cylinder. Nomenclature a, b inner and outer radii r radial coordinate c(r) volume fraction of material A c 0 , k, n material parameters in the volume fraction c(r) p a , p b internal and external pressures j a , j b internal and external electric potentials C ijkl i (i=1, 2) elastic modulus of the component e mij i (i=1, 2) piezoelectric tensor modulus of the component k mk i (i=1, 2) dielectric modulus of the component u radial displacement j electric potential e , r i ( ) e q i ( ) radial and hoop strains of the component e , r e q average radial and hoop strains of the cylinder s , r i ( ) s q , i ( ) s z i ( ) radial, hoop, and axial stresses of the component s , r s q , s z average radial, hoop, and axial stresses of the cylinder E , r i ( ) D r i ( ) radial electric field and electric displacement of the component E , r D r average radial electric field and electric displacement of the cylinder a(r), b(r), d(r), g(r), f (r), h(r), k(r) functions related to the volume fraction c(r)

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“…Recently, by assuming the elastic modulus and magnetic permeability into as power series forms (for example in [35], by setting also thoroughly researched [37][38][39][40]. However, all these works ignored the influences from Poisson's ratio which has been reflected in [41][42][43] by analyzing the radical displacements and stress components of the mechanical loaded FGM tubes under a uniform magnetic field. Furthermore, the FGMs can be literally and theoretically considered as being composed by grading its different components in certain directions by some specific volume fraction forms; but if the expressions of the components' volume fractions are set with inappropriate forms, rather complex mathematical derivation efforts and complicated results originate [44].…”

Section: Introductionmentioning

confidence: 99%

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

Dui

Pan

et al. 2018

Appl. Math. Mech.-Engl. Ed.

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In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subjected to uniform magnetic field and inner-pressurized loads are studied. Rather than directly assuming the material constants into some certain function forms as displayed in pre-researches, we firstly give the volume fractions of different constituents of the FGM cylinder and then determine the expressions of material constants. By the use of the Voigt method the corresponding analytical solutions of displacements in radical direction, the strain and stress components and the perturbation magnetic field vector are derived by the following. In numerical part, 1 the influences of volume fraction on displacement, stain and stress components and the magnetic perturbation filed vector are investigated; indicated by the results, we can conclude that the Poisson's ratio has a significant effect on the FGM cylinder's mechanical behaviors. Moreover, by some appropriate choices of the material constants it can be found that the obtained results in this paper can reduce to some special cases given in previous literatures.

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An elasticity solution for functionally graded thick-walled tube subjected to internal pressure

Cited by 49 publications

References 15 publications

Thermoelastic Analysis of a Functionally Graded Rotating Thick-Walled Tube Subjected to Mechanical and Thermal Loads

Thermoelastic Analysis of a Functionally Graded Rotating Thick-Walled Tube Subjected to Mechanical and Thermal Loads

Revisiting the electroelastic solution for an FGPM thick-walled cylinder subjected to mechanical and electric loadings

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

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