Thermal Stresses—Advanced Theory and Applications

Hetnarski, Richard B.; Eslami, M. R.

doi:10.1007/978-3-030-10436-8

Cited by 156 publications

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“…Figure shows an excellent agreement between the exact and mesh‐free results in temperature distribution of cylinders.…”

Section: Resultssupporting

confidence: 55%

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Thermoelastic vibration analysis of functionally graded wavy carbon nanotube‐reinforced cylinders

Moradi‐Dastjerdi

Payganeh

2017

Polymer Composites

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In this study, free vibration behavior of functionally graded carbon nanotube‐reinforced composite (FG‐CNTRC) cylinders subjected to uniform temperature environment or thermal gradient loading is investigated by a mesh‐free method. The nanocomposite cylinders are made of a polymer matrix and wavy single‐walled carbon nanotubes (SWCNTs). The volume fraction of carbon nanotubes (CNTs) are assumed variable along the radial direction of the axisymmetric cylinder. Also, material properties of the polymer and CNT are assumed temperature‐dependent and mechanical properties of the nanocomposite are estimated by a micromechanical model in volume fraction form. In the mesh‐free analysis, moving least squares shape functions are used to approximate displacement field in the weak form of motion equation and the transformation method is used to impose essential boundary conditions. The material properties and natural frequency of the nanocomposite cylinders are derived after the derivation of cylinder temperature and by considering of the temperature and location. Effects of CNT distribution pattern and volume fraction, thermal, cylinder dimensions and CNT aspect ratio and waviness are investigated on the vibration behavior of the nanocomposite cylinders. POLYM. COMPOS., 39:E826–E834, 2018. © 2017 Society of Plastics Engineers

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“…Figure shows an excellent agreement between the exact and mesh‐free results in temperature distribution of cylinders.…”

Section: Resultssupporting

confidence: 55%

“…Now, to examine the applied mesh‐free method in temperature distribution, consider a hollow cylinder with inside and outside temperatures of T i and T o , respectively. The steady‐state one dimensional temperature distribution of cylinders with no heat generation is as :

T = \frac{T_{i} - T_{o}}{\ln (r_{o} - r_{i})} \ln (r_{o} - r) + T_{b}

…”

Section: Resultsmentioning

confidence: 99%

Thermoelastic vibration analysis of functionally graded wavy carbon nanotube‐reinforced cylinders

Moradi‐Dastjerdi

Payganeh

2017

Polymer Composites

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“…This is underpinned by the fact that model studies on thermal expansion of 4 mm diameter spheres versus 4 mm diameter cylindrical rods, subjected to a stepwise temperature change at the boundary, show a sphere:cylinder strain ratio of ~0.8 [cf. Hetnarski et al ., ]. The usefulness of our approach is also supported by the fact that our simple radially symmetric model explains our experimental data well (see details in section 4.2.2), using a single diffusion coefficient over all boundary conditions.…”

Section: Discussionmentioning

confidence: 99%

“…Displacements u are only possible in the radial direction, and the principal strains are related to radial displacement via

ε_{normalr normalr} = \frac{\partial u}{\partial r}

and

ε_{normalϕ normalϕ} = ε_{normalγ normalγ} = \frac{u}{r}

(note that we take compression as positive and radial displacement to be positive inward). By analogy with the thermo‐elastic equations for an isotropic sphere, subjected to an instantaneously imposed fixed temperature at its external surface [e.g., Hetnarski et al ., ], the following relations for the displacement and total stress fields inside the sample may be obtained (see details of derivation in Appendix A):

u ((),, r, t) = prefix- \frac{α}{r^{2}} \frac{1 + ν}{1 - ν} true {true\int}_{0}^{r} r^{2} θ ((),, r, t) d r - 2 \frac{α r}{b^{3}} \frac{1 - 2 ν}{1 - ν} true {true\int}_{0}^{b} r^{2} θ ((),, r, t) d r + r ((), 1 - 2 ν) \frac{P}{E}

σ_{r r} ((),, r, t) = \frac{- α E}{1 - ν} ({}, \frac{2}{b^{3}} true {true\int}_{0}^{b} r^{2} θ ((),, r, t) d r - \frac{2}{r^{3}} true {true\int}_{0}^{r} r^{2} θ ((),, r, t) d r) + P

σ_{ϕ ϕ} ((),, r, t) = \frac{- α E}{1 - ν} ({}, \frac{1}{r^{3}} true {true\int}_{0}^{r} r^{2} θ ((),, r, t) d r + \frac{2}{b^{3}} true true\int)

…”

Section: Theoretical Modelsmentioning

confidence: 99%

Coupling of swelling, internal stress evolution, and diffusion in coal matrix material during exposure to methane

2017

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We construct theoretical models for time‐dependent swelling of coal matrix material upon adsorption of a single gas, taking into account a coupling between stress, strain, chemical potential, and diffusion. Two models are developed. The first (model A) corresponds to diffusion and hence swelling rates being controlled by the jump frequency of adsorbed molecules between closely spaced adsorption sites and the second (model B) to transport controlled by diffusion of unadsorbed molecules through diffusion paths linking distant adsorption sites. To test these models, we performed axial swelling experiments on a single 4 mm sized cylindrical sample of medium volatile bituminous coal, exposed to CH4 at pressures up to 40 MPa, at 40°C, using 1‐D, high‐pressure dilatometry. The models were calibrated to the experimental data by adjustment of a single‐valued diffusion coefficient, independent of gas pressure and adsorbed concentration. The results show that the data can be accurately explained only by model B. The implication is that the gas transport, the associated adsorption, and hence time‐dependent swelling are controlled by the diffusion of unadsorbed molecules and not by molecules jumping between the adjacent adsorption sites. Our model describes a full coupling between stress, strain, sorption, and diffusion in coal matrix material in terms of parameters that have clear physical meaning and are easily obtained from sorption and swelling experiments on coal of any rank exposed to any gas. It therefore offers an important tool for modeling permeability evolution with time during (enhanced) coalbed methane operations.

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“…Based on Hooke's law, considering the thermal effects, the stress‐strain relations may be written as []

\begin{matrix} right σ_{x} & = & left E (r, T) (ε_{x} - α (r, T) Δ T) = E (r, T) \{\frac{d u}{d x} - \frac{w}{R} + \frac{1}{2} {(\frac{d w}{d x})}^{2} + F_{1} \frac{d^{2} w}{d x^{2}} + F_{2} \frac{d φ}{d x} - α (r, T) Δ T\} \\ right τ_{x y} & = & left \frac{E (r, T)}{2 \{1 + ν (r, T)\}} \frac{\partial F_{1}}{\partial y} (\frac{d w}{d x} + φ) \\ right τ_{x z} & = & left \frac{E (r, T)}{2 \{1 + ν (r, T)\}} \frac{\partial F_{2}}{\partial z} (\frac{d w}{d x} + φ) \end{matrix}

…”

Section: Governing Equationsmentioning

confidence: 99%

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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Thermal Stresses—Advanced Theory and Applications

Cited by 156 publications

References 0 publications

Thermoelastic vibration analysis of functionally graded wavy carbon nanotube‐reinforced cylinders

Thermoelastic vibration analysis of functionally graded wavy carbon nanotube‐reinforced cylinders

Coupling of swelling, internal stress evolution, and diffusion in coal matrix material during exposure to methane

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

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