Nonlinear bending and vibration of functionally graded tubes resting on elastic foundations in thermal environment based on a refined beam model

Zhong, Jun; Fu, Yiming; Wan, Detao; Li, Yingli

doi:10.1016/j.apm.2016.03.031

Cited by 61 publications

(14 citation statements)

References 36 publications

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“…Based on the von Kármán strain‐displacement relations expressed for annular tubes, and circular curved beams, the non‐linear strain‐displacement components associated with the above displacement field of the shallow curved tubes are obtained as

\begin{matrix} right ε_{x} & = & left \frac{\partial u_{1}}{\partial x} - \frac{u_{3}}{R} + \frac{1}{2} {(\frac{\partial u_{3}}{\partial x})}^{2} = \frac{\partial u}{\partial x} - \frac{w}{R} + \frac{1}{2} {(\frac{\partial w}{\partial x})}^{2} + z (\frac{\partial φ}{\partial x} + \frac{1}{r^{2}} \frac{\partial φ_{1}}{\partial x} + r^{2} \frac{\partial φ_{2}}{\partial x}) \\ right γ_{x z} & = & left \frac{\partial u_{1}}{\partial z} + \frac{\partial u_{3}}{\partial x} = \frac{\partial w}{\partial x} + φ + (\frac{1}{r^{2}} - \frac{2 z^{2}}{r^{4}}) φ_{1} + (r^{2} + 2 z^{2}) φ_{2} \\ right γ_{x y} & = & left \frac{\partial u_{1}}{\partial y} + \frac{\partial u_{2}}{\partial x} = 2 y z (φ_{2} - \frac{φ_{1}}{r^{4}}) \\ right γ_{r x} & = & left γ_{x z} \end{matrix}

…”

Section: Governing Equationsmentioning

confidence: 99%

“…For functionally graded materials, temperature-dependent thermal and mechanical material properties may vary to follow the power law function distribution in the radial direction as follow [8][9][10]…”

Section: Governing Equationsmentioning

confidence: 99%

“…Based on the von Kármán strain-displacement relations expressed for annular tubes, [8][9][10][11] and circular curved beams, [12] the non-linear strain-displacement components associated with the above displacement field of the shallow curved tubes are obtained as…”

Section: Governing Equationsmentioning

confidence: 99%

“…carried out a study on the nonlinear thermal buckling and post‐buckling analysis of elastic FGM tubes with immovable pined‐pined end conditions by means of the two‐step perturbation technique based on a refined beam model. Zhong et al . carried out studies for in‐plane nonlinear free vibrations and static bending behavior of elastic FGM pinned tubes with immovable end conditions resting on two‐parameters elastic foundation based on a refined beam model in thermal environments.…”

Section: Introductionmentioning

confidence: 99%

“…Fu et al [9] carried out a study on the nonlinear thermal buckling and post-buckling analysis of elastic FGM tubes with immovable pined-pined end conditions by means of the two-step perturbation technique based on a refined beam model. Zhong et al [10] carried out studies for in-plane nonlinear free vibrations and static bending behavior of elastic FGM pinned tubes with immovable end conditions resting on two-parameters elastic foundation based on a refined beam model in thermal environments. She et al [11] introduced the new analytical solutions for nonlinear static bending and thermal post-buckling analysis of the FGM elastic tubes with immovable clamped-clamped end conditions considering thermal effects by using the two-step perturbation method.…”

Section: Introductionmentioning

confidence: 99%

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Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method

2018

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In the present investigation, geometrically nonlinear response of a shallow curved tube subjected to thermal loading is analyzed. The tube is made of a functionally graded material (FGM), where properties are distributed across the tube radius. Thermomechancal properties of the constituents are assumed to be temperature dependent. The simple case of uniform temperature rise loading is considered. A higher order displacement field is considered for the tube which satisfies the conditions of zero tangential tractions on the inner and outer surfaces of the tube. With the aid of von Kármán strain‐displacement relations, linear thermoelastic constitutive law, and Hamilton's principle the governing equations of the tube are obtained. These equations are reduced to new two coupled equations for the case of axially immovable tubes. These new equations are solved using the two step perturbation technique for pinned and clamped tubes. Closed form expressions are provided to estimate the deflections in the FGM temperature dependent curved tubes under uniform thermal load. The effect of boundary conditions, temperature dependency of material properties, and geometrical properties are discussed via numerical examples.

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