• Structural Engineering and Mechanics
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• v.10 no.4
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• pp.337-357
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• 2000

Analytical formulations and solutions for the first time, to the stability analysis of a simply supported composite and sandwich plates based on a higher order refined theory, developed by the first author and already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations which account for the effects of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of inplane displacements with respect to the thickness coordinate - thus modelling the warping of transverse cross sections more accurately and eliminating the need for shear correction coefficients. The equations of equilibrium are obtained using the Principle of Minimum Potential Energy (PMPE). The comparison of the results using this higher order refined theory with the available elasticity solutions and the results computed independently using the first order and the other higher order theories developed by other investigators and available in the literature shows that this refined theory predicts the critical buckling load more accurately than all other theories considered in this paper. New results for sandwich laminates are also presented which may serve as a benchmark for future investigations.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.17 no.1
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• pp.21-30
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• 2007

To establish the Fourier-transform infra-red spectrophotometry (FTIR) direct-on-filter(DOF) technique as a useful analytical method for quartz in respirable dust samples, influence of the interference should be corrected. This study was designed to compare three methods of correction for cristobalite when quantifying the content of quartz, including the least square, the optimum choice and the spectral subtraction methods. Respirable dust, created in a dust chamber containing the standard material of quartz, cristobalite was collected using a cyclone equipped with a 25 mm, $0.8{\mu}m$ pore size DM filter as a collection medium. The quartz weights overestimated about 100% when mixed of cristobalite by measure using 799 cm-1 absorption peak of quartz. The quartz weights appeared over estimated by optimum choice, spectral subtraction and least square method in mixtures of 33% cristobalite were 90.3%, 60.1% and about 4.3%, respectively. The least square method have been adopted to correction methods of cristobalite and satisfactory results have been obtained. The results of this study suggest that, when correcting for effect of cristobalite on quantitative analysis of quartz in respirable dust by FTIR direct-on-filter method, the least square method produce the most unbiased results compared with those of other correction methods.

• Journal of Adhesion and Interface
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• v.5 no.2
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• pp.22-36
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• 2004

Several in-situ testing methods of adhesively bonded joints under static short-time tensile loading are critically analyzed in terms of experimental procedure and data evaluation. Due to its rather homogeneous stress state across the glue line, the tensile-shear test with thick single-lap specimens, according to ISO 11003-2, has become the most important test process for the determination of realistic materials parameters. This basic method, which was improved in both, the experimental part by stepped adherends and easily attachable extensometers and the evaluation procedure by numeric substrate deformation correction and test simulation based on the finite element method (FEM), is therefore demonstrated by application to several kinds of adhesives and metallic adherends. Multi-axial load decreases the strength of a joint. This effect, which is illustrated by an experimental comparison, impedes the derivation of realistic mechanical characteristics from measured force-displacement curves. It is shown by numeric modeling that tensile-shear tests with thin plate substrates according to ISO 4587, which are widely used for quick industrial quality assurance, reveal an inhomogeneous stress state, especially because of relatively large adherend deformation. Complete experimental determination of the elastic properties of bonded joints requires independent measurement of at least two characteristics. As the thick-adherend tensile-shear test directly yields the shear modulus, the tensile butt-joint test according to ISO 6922 represents the most obvious complement of the test programme. Thus, validity of analytical correction formulae proposed in literature for the derivation of realistic materials characteristics is verified by numeric simulation. Moreover, the influence of the substrate deformation is examined and a FEM correction method introduced.

• Coupled systems mechanics
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• v.12 no.3
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• pp.199-220
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• 2023

This article presents a new analytical model to study the effect of porosity on the shear correction factors (SCFs) of functionally graded porous beams (FGPB). For this analysis, uneven and logarithmic-uneven porosity functions are adopted to be distributed through the thickness of the FGP beams. Critical to the application of this theory is a determination of the correction factor, which appears as a coefficient in the expression for the transverse shear stress resultant; to compensate for the assumption that the shear strain is uniform through the depth of the cross-section. Using the energy equivalence principle, a general expression is derived from the static SCFs in FGPB. The resulting expression is consistent with the variationally derived results of Reissner's analysis when the latter are reduced from the two-dimensional case (plate) to the one-dimensional one (beam). A convenient algebraic form of the solution is presented and new study cases are given to illustrate the applicability of the present formulation. Numerical results are presented to illustrate the effect of the porosity distribution on the (SCFs) for various FGPBs. Further, the law of changing the mechanical properties of FG beams without porosity and the SCFare numerically validated by comparison with some available results.

• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.1-11
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• 2024

This article introduces a novel analytical model for examining the impact of porosity on shear correction factors (SCFs) in functionally graded porous beams (FGPB). The study employs uneven and logarithmic-uneven modified porosity-dependent power-law functions, which are distributed throughout the thickness of the FGP beams. Additionally, a modified exponential-power law function is used to estimate the effective mechanical properties of functionally graded porous beams. The correction factor plays a crucial role in this analysis as it appears as a coefficient in the expression for the transverse shear stress resultant. It compensatesfor the assumption that the shear strain is uniform across the depth of the cross-section. By applying the energy equivalence principle, a general expression for static SCFs in FGPBs is derived. The resulting expression aligns with the findings obtained from Reissner's analysis, particularly when transitioning from the two-dimensional case (plate) to the one-dimensional case (beam). The article presents a convenient algebraic form of the solution and provides new case studies to demonstrate the practicality of the proposed formulation. Numerical results are also presented to illustrate the influence of porosity distribution on SCFs for different types of FGPBs. Furthermore, the article validates the numerical consistency of the mechanical property changesin FG beams without porosity and the SCF by comparing them with available results.

• Korean Journal of Computational Design and Engineering
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• v.18 no.6
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• pp.385-398
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• 2013

Opening wedge high tibial osteotomy (OWHTO) is widely used to treat unicompartmental osteoarthritis of the knee caused by degenerative deformations of the anatomical axes of the leg. However, since it is difficult to accurately plan the surgical degrees of adjustment such as coronal correction angle and tibial posterior slope angle to align the axes before the actual procedure, a number of studies have proposed analytical models to solve this problem. While previous analytical models for OWHTO were limited to specific cases, this study proposes an analytical osteotomy model (AOM) and a surgical planning system (SPS) that are suitable for a wide range of tibial morphologies and tibia conditions. The validity and generality of the model were verified in a total of 60 OWHTO cases. Results of the test showed that, as predicted, surgical degrees are affected quite significantly by tibia shape and slope of the resected surface. Comparison of the required surgical degrees and the degrees estimated from virtual surgery simulations using AOM showed a very small average difference of $0.118^{\circ}$. SPS, based on AOM, allows the operating surgeon to easily calculate surgical parameters needed to treat a patient.

• Journal of the Korean Chemical Society
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• v.30 no.6
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• pp.538-547
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• 1986

The 8 rare earth elements were determined in the monazite concentrates by X-ray fluorescence spectrometry. The spectral line overlapping interferences from the other elements were investigated and the correction methods of interferences were studied using line overlap coefficients. The coefficients were calculated from the ratios of the intensities measured at the diffracted angle (2${\theta}$) of the analytical lines of other elements to the intensity of pure rare earth oxide. The coefficients were used to correct the line overlaps by a regression analysis. The linearities of calibration curves from the corrected intensities were remarkably improved, and their standard deviations were decreased. The analytical results agreed with that of the inductively coupled plasma(ICP) spectrometry within an allowable error range.

• Wind and Structures
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• v.34 no.1
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• pp.43-58
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• 2022

The BARC flow is studied via Direct Numerical Simulation at a relatively low turbulent Reynolds number, with focus on the geometrical representation of the leading-edge (LE) corners. The study contributes to further our understanding of the discrepancies between existing numerical and experimental BARC data. In a first part, rounded LE corners with small curvature radii are considered. Results show that a small amount of rounding does not lead to abrupt changes of the mean fields, but that the effects increase with the curvature radius. The shear layer separates from the rounded LE at a lower angle, which reduces the size of the main recirculating region over the cylinder side. In contrast, the longitudinal size of the recirculating region behind the trailing edge (TE) increases, as the TE shear layer is accelerated. The effect of the curvature radii on the turbulent kinetic energy and on its production, dissipation and transport are addressed. The present results should be contrasted with the recent work of Rocchio et al. (2020), who found via implicit Large-Eddy Simulations at larger Reynolds numbers that even a small curvature radius leads to significant changes of the mean flow. In a second part, the LE corners are fully sharp and the exact analytical solution of the Stokes problem in the neighbourhood of the corners is used to locally restore the solution accuracy degraded by the singularity. Changes in the mean flow reveal that the analytical correction leads to streamlines that better follow the corners. The flow separates from the LE with a lower angle, resulting in a slightly smaller recirculating region. The corner-correction approach is valuable in general, and is expected to help developing high-quality numerical simulations at the high Reynolds numbers typical of the experiments with reasonable meshing requirements.

• Journal of Radiation Protection and Research
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• v.28 no.1
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• pp.19-24
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• 2003

The self-attenuation factor for an $^{198}Au$ sample and the 0.412 MeV gamma-ray penetration ratio in the circular Al-cover of the radiation detector have been determined using an analytical solution and MCNP code. The results show that the self-attenuation factors obtained from the analytical solution coincide with those of MCNP code for all but the Au sample with the relatively larger radius. Then the maximum difference between the two methods appears to be 9 % in the Au sample of 1.5 mm radius. It also is revealed that the analytical solutions of the 0.412 MeV gamma-ray penetration ratio in the Al-cover of 7.62 cm radius are consistent with those of the MCNP code within the standard deviation.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.593-605
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• 2023

This work presents a comparison between analytical and finite element analysis for bending of porous sandwich functionally graded material (FGM) plates. The plate is rectangular and simply supported under static sinusoidal loading. Material properties of FGM are assumed to vary continuously across the face sheets thickness according to a power-law function in terms of the volume fractions of the constituents while the core is homogeneous. Four types of porosity are considered. A refined higher-order shear with normal deformation theory is used. The number of unknowns in this theory is five, as against six or more in other shear and normal deformation theories. This theory assumes the nonlinear variation of transverse shear stresses and satisfies its nullity in the top and bottom surfaces of the plate without the use of a shear correction factor. The governing equations of equilibrium are derived from the virtual work principle. The Navier approach is used to solve equilibrium equations. The constitutive law of the porous FGM sandwich plate is implemented for a 3D finite element through a subroutine in FORTRAN (UMAT) in Abaqus software. Results show good agreement between the finite element model and the analytical method for some results, but the analytical method keeps giving symmetric results even with the thickness stretching effect and load applied to the top surface of the sandwich.