Stochastic heat conduction analysis of a functionally graded annular disc with spatially random heat transfer coefficients

Chiba, Ryoichi

doi:10.1016/j.apm.2007.11.014

Cited by 35 publications

(16 citation statements)

References 17 publications

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“…[4]. Chiba [5] analytically derived the second-order statistics in an axisymmetrically heated, functionally graded, annular disc with spatially random heat transfer coefficients on the upper and lower surfaces using an integral transform method and a perturbation method. Wang and Noda [6] investigated the fracture behavior of a cracked, functionally graded actuator on a substrate under thermal load.…”

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confidence: 99%

Stress analysis of functionally graded rotating discs: analytical and numerical solutions

2011

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This study deals with stress analysis of annular rotating discs made of functionally graded materials (FGMs). Elasticity modulus and density of the discs are assumed to vary radially according to a power law function, but the material is of constant Poisson's ratio. A gradient parameter n is chosen between 0 and 1.0. When n = 0, the disc becomes a homogeneous isotropic material. Tangential and radial stress distributions and displacements on the disc are investigated for various gradient parameters n by means of the diverse elasticity modulus and density by using analytical and numerical solutions. Finally, a homogenous tangential stress distribution and the lowest radial stresses along the radius of a rotating disc are approximately obtained for the gradient parameter n = 1.0 compared with the homogeneous, isotropic case n = 0. This means that a disc made of FGMs has the capability of higher angular rotations compared with the homogeneous isotropic disc.

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confidence: 99%

Stress analysis of functionally graded rotating discs: analytical and numerical solutions

2011

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“…The dynamic thermo-elastic behavior of rod was modeled using GN theory of coupled thermo-elasticity. The stochastic heat conduction analysis was analytically studied in a functionally graded annular disc with spatially random heat transfer coefficients (HTCs) using multilayer assumption with spatially constant material properties and spatially constant but random HTCs in each layer by Chiba [15]. Also, the applicability of derived analytical solution was compared with the results obtained by direct Monte Carlo simulation.…”

Section: Introductionmentioning

confidence: 99%

Transient analysis of thermo-elastic waves in thick hollow cylinders using a stochastic hybrid numerical method, considering Gaussian mechanical properties

Hosseini

Shahabian

2011

Applied Mathematical Modelling

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a b s t r a c tThis article attempts to study the stochastic coupled thermo-elasticity of thick hollow cylinders subjected to thermal shock loading considering uncertainty in mechanical properties. The thermo-elastic governing equations based on Green-Naghdi theory (without energy dissipation) are stochastically solved using a hybrid numerical method (combined Galerkin finite element and Newmark finite difference methods). The mechanical properties are considered as random variables with Gaussian distribution, which are generated using Monte Carlo simulation method with various coefficients of variations (COVs). The effects of uncertainty in mechanical properties with various coefficients of variations on thermo-elastic wave propagation are studied in detail. Also, the maximum, mean and variance of temperature, displacement and stresses are illustrated across thickness of cylinder in various times.

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“…In the case of the functionally graded materials, it is also possible to find a minor number of works. Among them, one may refer the studies published by Chiba and Sugano [8], Chiba [9], and Rahman and Chakraborty [10].…”

Section: Introductionmentioning

confidence: 99%

Toward Variability Characterization and Statistic Models’ Constitution for the Prediction of Exponentially Graded Plates’ Static Response

2018

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Functionally graded composite materials may constitute an advantageous alternative to engineering applications, allying a customized tailoring capability to its inherent continuous properties transition. However, these attractive characteristics must account for the uncertainty that affects these materials and their structures’ physical quantities. Therefore, it is important to analyze how this uncertainty will modify the foreseen deterministic response of a structure that is built with these materials, identifying which of the parameters are responsible for a greater impact. To pursue this main objective, the material and geometrical parameters that characterize a plate made of an exponentially graded material are generated according to a random multivariate normal distribution, using the Latin hypercube sampling technique. Then, a set of finite element analyses based on the first-order shear deformation theory are performed to characterize the linear static responses of these plates, which are further correlated to the input parameters. This work also considers the constitution of statistic models in order to allow their use as alternative prediction models. The results show that for the plates that were analyzed, the uncertainty associated with the elasticity modulus of both phases is mainly responsible for the maximum transverse deflection variability. The effectiveness of the statistical models that are built are also shown.

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Stochastic heat conduction analysis of a functionally graded annular disc with spatially random heat transfer coefficients

Cited by 35 publications

References 17 publications

Stress analysis of functionally graded rotating discs: analytical and numerical solutions

Stress analysis of functionally graded rotating discs: analytical and numerical solutions

Transient analysis of thermo-elastic waves in thick hollow cylinders using a stochastic hybrid numerical method, considering Gaussian mechanical properties

Toward Variability Characterization and Statistic Models’ Constitution for the Prediction of Exponentially Graded Plates’ Static Response

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