• Structural Engineering and Mechanics
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• v.67 no.5
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• pp.527-544
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• 2018

In this paper, the effect of homogenization models on stress analysis is presented for functionally graded plates (FGMs). The derivation of the effective elastic proprieties of the FGMs, which are a combination of both ceramic and metallic phase materials, is of most of importance. The majority of studies in the last decade, the Voigt homogenization model explored to derive the effective elastic proprieties of FGMs at macroscopic-scale in order to study their mechanical responses. In this work, various homogenization models were used to derive the effective elastic proprieties of FGMs. The effect of these models on the stress analysis have also been presented and discussed through a comparative study. So as to show this effect, a refined plate theory is formulated and evaluated, the number of unknowns and governing equations were reduced by dividing the transverse displacement into both bending and shear parts. Based on sinusoidal variation of displacement field trough the thickness, the shear stresses on top and bottom surfaces of plate were vanished and the shear correction factor was avoided. Governing equations of equilibrium were derived from the principle of virtual displacements. Analytical solutions of the stress analysis were obtained for simply supported FGM plates. The obtained results of the displacements and stresses were compared with those predicted by other plate theories available in the literature. This study demonstrates the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Finally, this study offers benchmark results for the multi-scale analysis of functionally graded plates.

• Structural Engineering and Mechanics
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• v.85 no.1
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• pp.105-118
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• 2023

The present work is an attempt to develop a simple and accurate finite element formulation for the assessment of thermal shock/thermally induced vibrations in pretwisted and tapered functionally graded material thin (FGM) blades obtained from Voigt and local representative volume elements (LRVE) homogenization models, based on neutral surface approach. The neutral surface of the FGM blade does not coincide with its mid-surface. A finite element model (FEM) is developed using first-order shear deformation theory (FSDT) and the FGM turbine blade is modelled according to the shallow shell theory. The top and the bottom layers of the FGM blade are made of pure ceramic and pure metal, respectively and temperature-dependent material properties are functionally graded in the thickness direction, the position of the neutral surface also depends on the temperature. The material properties are estimated according to two different homogenization models viz., Voigt or LRVE. The top layer of the FGM blade is subjected to high temperature and the bottom surface is either thermally insulated or kept at room temperature. The solution of the nonlinear profile of the temperature in the thickness direction is obtained from the Fourier law of heat conduction in the unsteady state. The results obtained from the present FEM are compared with the benchmark examples. Next, the effect of angle of twist, intensity of thermal shock, variable chord and span and volume fraction index on the transient response due to thermal shock obtained from the two homogenization models viz., Voigt and LRVE scheme is investigated. It is shown that there can be a significant difference in the transient response calculated by the two homogenization models for a particular set of material and geometric parameters.

• Geomechanics and Engineering
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• v.16 no.3
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• pp.257-271
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• 2018

In this paper, the effect of the homogenization models on buckling and free vibration is presented for simply supported functionally graded plates (FGM) resting on elastic foundation. The majority of investigations developed in the last decade, explored the Voigt homogenization model to predict the effective proprieties of functionally graded materials at the macroscopic-scale for FGM mechanical behavior. For this reason, various models have been used to derive the effective proprieties of FGMs and simulate thereby their effects on the buckling and free vibration of FGM plates based on comparative studies that may differ in terms of several parameters. The refined plate theory, as used in this paper, is based on dividing the transverse displacement into both bending and shear components. This leads to a reduction in the number of unknowns and governing equations. Furthermore the present formulation utilizes a sinusoidal variation of displacement field across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the buckling and free vibration analysis are obtained for simply supported plates. The obtained results are compared with those predicted by other plate theories. This study shows the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Comprehensive visualization of results is provided. The analysis is relevant to aerospace, nuclear, civil and other structures.

• Nuclear Engineering and Technology
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• v.51 no.5
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• pp.1209-1217
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• 2019

Due to the limitation of the computers, the conventional homogenization method is based on many assumptions and approximations, and some tough problems such as energy spectrum and boundary condition are faced. To deal with those problems, the Monte Carlo global homogenization is adopted. The Reactor Monte Carlo code RMC is used to study the global homogenization method, and the one-step global homogenization method is proposed. The superimposed mesh geometry is also used to divide the physical models, leading to better geometric flexibility. A set of multigroup homogenization cross sections is online generated for each mesh under the real neutron energy spectrum and boundary condition, the cross sections are adjusted by the superhomogenization method, and no leakage correction is required. During the process of superhomogenization, the author-developed reactor core program NLSP3 is used for global calculation, so the global flux distribution and equivalent homogenization cross sections could be solved simultaneously. Meanwhile, the calculated homogenization cross section could accurately reconstruct the non-homogenization flux distribution and could also be used for fine calculation. This one-step global homogenization method was tested by a PWR assembly and a small reactor model, and the results show the validity.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.3
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• pp.588-594
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• 1998

Reliable three-dimensional models of woven fabric composites had scarcely been proposed for their geometric complexity. Simplified models, mostly one- or two-dimensional, currently used are not considered effective enough because of their oversimplifications. In this paper, the equivalent thermal conductivities and elasticity properties of woven fabric composites are computed using homogenization technique. The computational results show that the strength and thermal conductivity linearly increase with fiber volume fraction and that the variations of undulation of fibers has little effect on equivalent material properties. Homogenization technique is proved useful in the study of woven fabric composites and may find a lot more applications in the area.

• Journal of Environmental Science International
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• v.26 no.4
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• pp.421-432
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• 2017

In this study, we examined the suitability of ten disinfection models for predicting the inactivation of Artemia sp. via single or combined physical and chemical treatments. The effect of Hydraulic Retention Time (HRT) on the inactivation of Artemia sp. was examined experimentally. Disinfection models were fitted to the experimental data by using the GInaFiT plug-in for Microsoft Excel. The inactivation model were evaluated on the basis of RMSE (Root Mean Square Error), SSE (mean Sum Square Error) and $r^2$. An inactivation model with the lowest RMSE, SSE and $r^2$ close to 1 was considered the best. The Weibull+Tail model was found to be the most appropriate for predicting the inactivation of Artemia sp. via electrolytic treatment and electrolytic-ultrasonic combined treatment. The Log-linear+Tail model was the most appropriate for modeling inactivation via homogenization and combined electrolytic-homogenization treatment. The double Weibull disinfection model was the most suitable for the predicting inactivation via ultrasonic treatment.

• Geomechanics and Engineering
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• v.22 no.1
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• pp.65-80
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• 2020

This paper presents a theoretical investigation on the response of the thermo-mechanical bending of FG plate on variable elastic foundation. A quasi-3D higher shear deformation theory is used that contains undetermined integral forms and involves only four unknowns to derive. The FG plates are supposed simply supported with temperature-dependent material properties and subjected to nonlinear temperature rise. Various homogenization models are used to estimate the effective material properties such as temperature-dependent thermoelastic properties. Equations of motion are derived from the principle of virtual displacements and Navier's solution is used to solve the problem of simply supported plates. Numerical results for deflections and stresses of FG plate with temperature-dependent material properties are investigated. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of FG thick plates.

• Nuclear Engineering and Technology
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• v.49 no.7
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• pp.1379-1387
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• 2017

This paper presents a comparison of homogenization techniques implemented in the APOLLO3 platform for transport core calculations: standard scalar flux weighting and new flux-moment homogenization, in different combinations with (or without) leakage models. Besides the historical B1-homogeneous model, a new B-heterogeneous one has indeed been implemented recently in the two/three-dimensional-transport solver using the method of characteristics. First analyses have been performed on a very simple Sodium Fast Reactor core with a regular hexagonal lattice. They show that using the heterogeneous leakage model in association with flux-moment homogenization strongly improves the prediction of $k_{eff}$ and void reactivity effects. These good results are confirmed when the application is done to the fissile assemblies of the more complex CFV (Low Void Effect) core of the ASTRID (Advanced Sodium Technological Reactor for Industrial Demonstration) project of sodium-cooled fast breeder reactor (Generation IV).

• Computational Structural Engineering
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• v.8 no.3
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• pp.51-57
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• 1995

A simplified stress analysis of perforated plates was carried out using homogenization technique. Homogenization technique, which introduced miroscale expansion in the standard finite element method, reconstructed the plate with regularly placed holes into a set of macroscale and microscale models. The microscale model helped compute homogenized material constants of the unit cell, which were used to compute macroscale displacements in the macroscale model. Also it was possible to compute the stress field of the plate using the microscale model. It was found that reasonable equivalent material constants were computed and that the required degrees of freedom was drastically reduced when homogenization technique was employed in the stress analyses. The microscale modeling in the homogenization technique provided a useful concept of pre- and post-processing in the stress analysis of perforated plates.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.752-759
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• 2006

Conglomerates and core-stones are the typical composite geomaterials that are composed of a weak matrix and a strong pebble part. In general, we couldn't analyze the composite geomaterials by using emperical rock classification methods. In the study, a series of analyses of elastic behavior of composite geomaterials are carried out by using homogenization theory. 45-case models are made with considering 3 kind of factors such as gravel content, size and strength of matrix. Those are applicable to various composite geomaterials of conglomerates and core-stones. The size of analysis model is large enough to exceed REV.