• Advances in Computational Design
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• v.9 no.1
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• pp.39-52
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• 2024

If the governing differential equation arising from engineering problems is treated as an analytic, continuous and derivable function, it can be expanded by one point as a series of finite numbers. For the function to be zero for each value of its domain, the coefficients of each term of the same power must be zero. This results in a recursive relationship which, after applying the natural conditions or the boundary conditions, makes it possible to obtain the values of the derivatives of the function with acceptable accuracy. The elastoplastic analysis of an inhomogeneous thick sphere of metallic materials with linear variation of the modulus of elasticity, yield stress and Poisson's ratio as a function of radius subjected to internal pressure is presented. The Beltrami-Michell equation is established by combining equilibrium, compatibility and constitutive equations. Assuming axisymmetric conditions, the spherical coordinate parameters can be used as principal stress axes. Since there is no analytical solution, the natural boundary conditions are applied and the governing equations are solved using a proposed new method. The maximum effective stress of the von Mises yield criterion occurs at the inner surface; therefore, the negative sign of the linear yield stress gradation parameter should be considered to calculate the optimal yield pressure. The numerical examples are performed and the plots of the numerical results are presented. The validation of the numerical results is observed by modeling the elastoplastic heterogeneous thick sphere as a pressurized multilayer composite reservoir in Abaqus software. The subroutine USDFLD was additionally written to model the continuous gradation of the material.

• Structural Engineering and Mechanics
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• v.57 no.5
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• pp.823-835
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• 2016

Using the Complementary Functions Method (CFM), a general solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material (FGM) is presented. The mechanical properties are assumed to obey the exponential variations in the radial direction, and the Poisson's ratio is assumed to be constant, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the present paper, a semi-analytical iterative technique, one of the most efficient unified method, is employed to solve the heat conduction equation and the Navier equation. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and effective stress, as a function of radial direction, are obtained. Various material models from the literature are used and corresponding temperature distributions and stress distributions are computed. Verification of the proposed method is done using benchmark solutions available in the literature for some special cases and virtually exact results are obtained.

• Steel and Composite Structures
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• v.52 no.3
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• pp.377-390
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• 2024

Analyzing thermoelastic, elastoplastic, and residual stresses is pivotal for deepening our insights into material characteristics, particularly in the engineering of advanced materials like functionally graded materials (FGM). This research delves into these stress types within a thick-walled sphere composed of Al-SiC FGM, employing a detailed successive approximation method (SAM) to pinpoint stress distributions under varied loading scenarios. Our investigation centers on how the sphere's structure responds to different magnitudes of internal pressure. We discover that under various states-thermoelastic, elastoplastic, and residual-the radial stresses are adversely impacted, manifesting negative values due to the compressive nature induced by internal pressures. Notably, the occurrence of reverse yielding, observed at pressures above 410 MPa, merits attention due to its significant implications on the sphere's structural integrity and operational efficacy. Employing the SAM allows us to methodically explore the nuanced shifts in material properties across the sphere's thickness. This study not only highlights the critical behaviors of Al-SiC FGM spheres under stress but also emphasizes the need to consider reverse yielding phenomena to maintain safety and reliability in their application. We advocate for ongoing refinement of analytical techniques to further our understanding of stress behaviors in various FGM configurations, which could drive the optimized design and practical application of these innovative materials in diverse engineering fields.

• Journal of The Korean Astronomical Society
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• v.56 no.2
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• pp.287-292
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• 2023

This paper investigates the number of scatterings a photon undergoes in random walks before escaping from a medium. The number of scatterings in random walk processes is commonly approximated as τ + τ² in the literature, where τ is the optical thickness measured from the center of the medium. However, it is found that this formula is not accurate. In this study, analytical solutions in sphere and slab geometries are derived for both optically thin and optically thick limits, assuming isotropic scattering. These solutions are verified using Monte Carlo simulations. In the optically thick limit, the number of scatterings is found to be 0.5 τ² and 1.5 τ² in a sphere and slab, respectively. In the optically thin limit, the number of scatterings is ≈ τ in a sphere and ≈ τ (1 - γ - ln τ + τ) in a slab, where γ ≃ 0.57722 is the Euler-Mascheroni constant. Additionally, we present approximate formulas that reasonably reproduce the simulation results well in intermediate optical depths. These results are applicable to scattering processes that exhibit forward and backward symmetry, including both isotropic and Thomson scattering.

• Transactions of Materials Processing
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• v.21 no.5
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• pp.305-311
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• 2012

One of the main methods of building LNG tankers uses the Moss spherical tank design since it can be precisely analyzed with respect to reliability and safety of construction by stress analysis. Aluminum alloy 5083 is generally used in the Moss spherical tank design for the wall in constructing the LNG tanker. This aluminum alloy does not have low temperature brittleness, but has good corrosion resistance, good weldability, and excellent material properties for the application. The Moss spherical tank is constructed with several sections of A5083 thick plate with curved surfaces, which are welded together. It is essential to predict the amount of springback for the deformed thick plates in design to insure a reliable construction because the structure needs to be assembled into a perfect sphere. Unless the initial construction meets the design, there are additional processing costs for reworking to meet the specifications as well as a cost penalty paid to a consumer. In this paper, FE analyses were conducted to predict the amount of springback for various forming conditions and forming processes. The various forming processes were evaluated with respect to reducing springback and compared with the conventional forming process used for curved surfaces of thick Al plate.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.293-302
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• 2005

In this paper, the thick-walled laminated, orthotropic as well as bimaterial, composite hollow spheres under impact pressure are analyzed in detail by using the semi-discrete finite element method with the Houbolt time-integration scheme which results in unconditionally stable transient numerical results. Numerical results are obtained by using the self-constructed spherically symmetric (one-dimensional) and axially symmetric (two-dimensional) finite element programs, and compared with the previous solutions by other researchers, being shown some of which are incorrect. The finite element package Nastran is also adopted for numerical comparison.

• Electrical & Electronic Materials
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• v.8 no.2
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• pp.184-189
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• 1995

The electrical property of ultra thin PVA films(several hundreds .angs.-several .mu.m in thickness) formed by sphere bulb blowing technique, has been studied. The electrical conductivity of relatively thick films(>several thousands .angs.) has been very high and enhanced by the exposure either to high humidity of air or $NH_3$, which can be explained in terms of the role of ionic transport. The use of PVA films as NH$_{3}$ sensor is also proposed. In ultra thin PVA films less than 1500.angs., two conducting states ; high conducting and low conducting states, are observed. The nonlinear current-voltage characteristics in the low conducting state and the switching between these two states are also confirmed. These properties are discussed in terms of electronic conduction processes. The breakdown strength of the ultra thin PVA film is found to be very high(-30MV/cm), supporting the electron avalanche process in a thick polymer films.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1994.11a
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• pp.156-159
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• 1994

The electrical property of polyvinylalcohol (PVA) films (several hundreds ∼ several $\mu\textrm{m}$ in thickness) formed by sphere bulb blowing technique, has been studied. The electrical conductivity of relatively thick films (>several thousands ) has been very high and enhanced by the exposure either to high humidity fo air or NH$_3$. which can be explained in terms of the role of ionic transport. The use of PVA film as NH$_3$ sensor is also proposed. In PVA films less than 1500 , two conducting states: high conducting and low conducting states, are observed.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.10
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• pp.1499-1507
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• 2017

This paper presents an impact-based piezoelectric vibration energy harvester using a freely movable metal sphere and a piezoceramic fiber-based MFC (Macro Fiber Composite) as piezoelectric cantilever. The free motion of the metal sphere, which impacts both ends of the cavity in an aluminum housing, generates power across a cantilever-type MFC beam in response to low frequency vibration such as human-body-induced motion. Impacting force of the spherical proof mass is transformed into the vibration of the piezoelectric cantilever indirectly via the aluminum housing. A proof-of-concept energy harvesting device has been fabricated and tested. Effect of the indirect impact-based system has been tested and compared with the direct impact-based counterpart. Maximum peak-to-peak open circuit voltage of 39.8V and average power of $598.9{\mu}W$ have been obtained at 3g acceleration at 18Hz. Long-term reliability of the fabricated device has been verified by cyclic testing. For the improvement of output performance and reliability, various devices have been tested and compared. Using device fabricated with anodized aluminum housing, maximum peak-to-peak open-circuit voltage of 34.4V and average power of $372.8{\mu}W$ have been obtained at 3g excitation at 20Hz. In terms of reliability, housing with 0.5mm-thick steel plate and anodized aluminum gave improved results with reduced power reduction during initial phase of the cyclic testing.

• Journal of radiological science and technology
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• v.32 no.2
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• pp.213-218
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• 2009

A theoretical investigation has been carried out on how the energy width of the excited state of the nuclei is modulated when the $\gamma$-ray source is placed between two gold plates, at the center of the gold cylinder or the sphere. The width of the 81-keV level of $^{133}Cs$ is shown to become narrower by 3.7% at 4.2 K by reabsorption of $\gamma$ rays scattered backward from the parallel plates which are made of a 0.05-cm-thick, 3-cm-radius gold plates and separated from each other by 1.0 mm. With a 0.05-cm-thick, 5-cm-long, 1.0-mm-radius gold cylinder, we found that a width became narrower by 6.5%. In addition, when the nuclei is located in a spherical reflector of 1.0 mm in radius made of gold with a thickness of 0.5 mm. the level width is reduced by about 18.2% at a temperature 4.2 K. The results of this study indicates that the life-time of energy level was prolonged.