• Title/Summary/Keyword: Green's function

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Development of Green's Functions for Fatigue Damage Evaluation of CANDU Reactor Coolant System Components (CANDU형 원전 주요기기의 피로손상 평가를 위한 그린함수 개발)

  • Kim, Se Chang;Sung, Hee Dong;Choi, Jae Boong;Kim, Hong Key;Song, Myung Ho;Nho, Seung Hwan
    • Transactions of the Korean Society of Pressure Vessels and Piping
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    • v.7 no.4
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    • pp.38-43
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    • 2011
  • For the efficient and safe operation of nuclear power plant, evaluating quantitatively aging phenomenon of major components is necessary. Especially, typical aging parameters such as stresses and cumulative usage factors should be determined accurately to manage the lifetime of the plant facility. The 3-D finite element(FE) model is generated to calculate the aging parameters. Mechanical and thermal transfer functions called Green's functions are developed for the FE model with standard step input. The stress results estimated from transfer functions are verified by comparing with 3-D FE analyses results. Lastly, we suggest an effective fatigue evaluation methodology by using the transfer functions. The usefulness of the proposed fatigue evaluation methodology can be maximized by combining it with an on-line monitoring system.

Calculation of Stress Intensity Factors Using the Mixed Volume and Boundary Integral Equation Method (혼합 체적-경계 적분방정식법을 이용한 응력확대계수 계산)

  • Lee, Jung-Ki;Lee, Hyeong-Min
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.7
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    • pp.1120-1131
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    • 2003
  • A recently developed numerical method based on a mixed volume and boundary integral equation method is applied to calculate the accurate stress intensity factors at the crack tips in unbounded isotropic solids in the presence of multiple anisotropic inclusions and cracks subject to external loads. Firstly, it should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. Secondly, this method takes full advantage of the capabilities developed in FEM and BIEM. In this paper, a detailed analysis of the stress intensity factors are carried out for an unbounded isotropic matrix containing an orthotropic cylindrical inclusion and a crack. The accuracy and effectiveness of the new method are examined through comparison with results obtained from analytical method and volume integral equation method. It is demonstrated that this new method is very accurate and effective for solving plane elastostatic problems in unbounded solids containing anisotropic inclusions and cracks.

Analysis of Interfacial Surface Crack Perpendicular to the Surface (표면에 수직한 계면방향 표면균열의 해석)

  • 최성렬
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.2
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    • pp.277-284
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    • 1993
  • Interfacial surface crack perpendicular to the surface, which is imbedded into bonded quarter planes under single anti-plane shear load is analyzed. The problem is formulated using Mellin transform, form which single Wiener-Hopf equation is derived. By solving the equation stress intensity factor is obtained in closed form. This solution can be used as a Green's function to generate the solutions of other problems with the same geometry but of different loading conditions.

Elastic Analysis of Unbounded Solids with Anisotropic Inclusions (이방성 함유체를 포함하는 무한고체의 탄성해석)

  • Choe, Seong-Jun;Ra, Won-Seok;Lee, Jeong-Gi
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.23 no.11 s.170
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    • pp.1993-2006
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    • 1999
  • A Volume Integral Equation Method (VIEM) is applied for the effective analysis of elastic wave scattering problems and plane elastostatic problems in unbounded solids containing general anisotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids. Through the analysis of plane elastodynamic and elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions and voids.

Conversion of Recorded Ground Motion to Virtual Ground Motion Compatible to Design Response Spectra (계측 기록의 설계스펙트럼 부합 가상 지진 변환 방법)

  • Ji, Hae Yeon;Choi, Da Seul;Kim, Jung Han
    • Journal of the Earthquake Engineering Society of Korea
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    • v.25 no.1
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    • pp.33-42
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    • 2021
  • The design response spectrum presented in the seismic design standard reflects the characteristics of the tectonic environment at a site. However, since the design response spectrum does not represent the ground motion with a specific earthquake magnitude or distance, input ground motions for response history analysis need to be selected reasonably. It is appropriate to use observed ground motions recorded in Korea for the seismic design. However, recently recorded ground motions in the Gyeongju (2016) or Pohang (2017) earthquakes are not compatible with the design response spectrum. Therefore, it is necessary to convert the recorded ground motion in Korea to a model similar to the design response spectrum. In this study, several approaches to adjust the spectral acceleration level at each period range were tested. These are the intrinsic and scattering attenuation considering the earthquake environment, magnitude, distance change by the green function method, and a rupture propagation direction's directivity effect. Using these variables, the amplification ratio for the representative natural period was regressed. Finally, the optimum condition compatible with the design response spectrum was suggested, and the validation was performed by converting the recorded ground motion.

Preliminary strong ground motion simulation at seismic stations within nuclear power plant sites in South Korea by a scenario earthquake on the causative fault of 2016 Gyeongju earthquake

  • Choi, Hoseon
    • Nuclear Engineering and Technology
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    • v.54 no.7
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    • pp.2529-2539
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    • 2022
  • Stochastic and an empirical Green's function (EGF) methods are preliminarily applied to simulate strong ground motions (SGMs) at seismic stations within nuclear power plant (NPP) sites in South Korea by an assumed large earthquake with MW6.5 (scenario earthquake) on the causative fault of the 2016 Gyeongju earthquake with MW5.5 (mainshock). In the stochastic method, a ratio of spectral amplitudes of observed and simulated waveforms for the mainshock is assumed to be an adjustment factor. In the EGF method, SGMs by the mainshock are simulated assuming SGMs by the 2016 Gyeongju earthquake with MW5.0 (foreshock) as the EGF. To simulate SGMs by the scenario earthquake, a ratio of fault length to width is assumed to be 2:1 in the stochastic method, and SGMs by the mainshock are assumed to be EGF in the EGF method. The results are similar based on a bias of the simulated response spectra by the two methods, and the simulated response spectra by the two methods exceeded commonly standard design response spectra anchored at 0.3 g of NPP sites slightly at a frequency band above 4 Hz, but considerable attention to interpretation is required since it is an indirect comparison.

The Motion Response of an Oil Boom with Flexible Skirt (유연한 스커트를 가진 오일붐의 운동응답해석)

  • 성홍근;조일형;최항순
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.7 no.2
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    • pp.156-162
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    • 1995
  • A numerical method for a 2-D oil boom model considering the flexibility of skirt has been developed The neater is assumed rigid and the skirt is tensioned membrane having a point mass at its end The fluid motion is potential. The kinematic condition which demands the continuity of the displacement is imposed at the joint between the floater and the skirt. The dynamic condition for the point mass is imposed at the bottom end of the skirt. The numerical method is based on the Green's function method in the frame of linear potential theory. It finds it's solution simultaneously from the total system of three equations, integral equation, the equation of motion of the floater and the equilibrium equation of the deformation of the skirt. Integral equation is derived by applying the Green's theorem to radiation potential and Green's function. Proper descretization of those three equations leads to the system of a linear algebraic equation. Due to the flexibility of skirt the motion of floater can be diminished in some range of wave frequency and furthermore the mechanism of resonance of the oil boom can be changed. The motion responses of various oil booms have been compared varying the length of the skirt and the point mass. The numerical method has been validated indirectly from the good correspondence between the motion responses of the flexible skirt model and the rigid skirt model in low frequency limit.

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View-oriented and Green Marketing Characteristics of Apartment Advertisements on Newspapers (신문 아파트광고에 나타난 조망지향성과 그린마케팅의 속성)

  • Rho, Jae-Hyun;Kim, Ok-Kyung
    • Journal of the Korean Institute of Landscape Architecture
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    • v.34 no.6 s.119
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    • pp.87-100
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    • 2007
  • This study analyzed the key words in Korea's leading apartment brands and newspaper advertisements to examine especially their view-oriented advertising characteristics and green marketing properties. Four study topics were established and examined for this purpose. The following are the results; 1. The key words on apartment brands and catch phrases are $\ulcorner$emotion-oriented$\lrcorner$ words, such as taste, pride, and happiness, and $\ulcorner$environment-oriented$\lrcorner$ to appeal to customers with beautiful views of the nature. Also key words on newspaper advertisement headlines stress views for $\ulcorner$environment-oriented$\lrcorner$ characteristics as well as $\ulcorner$emotion-oriented$\lrcorner$ characteristics for elegance and luxury, and $\ulcorner$function-oriented$\lrcorner$ characteristics for the future. Views, nature and park are key words and everything about illustration that are especially emphasized even on the headlines of newspaper advertisements. 2. Unlike brands or headlines, sub-headlines and body copies stress $\ulcorner$modern-oriented$\lrcorner$ characteristics for life, culture, and accessibility, followed by $\ulcorner$emotion-oriented$\lrcorner$ characteristics. Key words on caption were also highly $\ulcorner$modern-oriented$\lrcorner$, followed by $\ulcorner$environment-oriented$\lrcorner$ and $\ulcorner$function-oriented$\lrcorner$ characteristics for practical aspects. 3. In result of $X^2-test$, $\ulcorner$environment-oriented$\lrcorner$ key words that convey good views, naturalism, parks, and nature are the major representation of green marketing strategies of apartment brands and newspaper advertisements. However, brands were strongly $\ulcorner$emotion-oriented$\lrcorner$, whereas captions were $\ulcorner$modern-oriented$\lrcorner$ and body copies were $\ulcorner$investment-oriented$\lrcorner$. Both apartment brands and advertisements were consistently $\ulcorner$environment-oriented$\lrcorner$, but were not consistent in other factors. 4. Different parts of newspaper advertisements are focusing on green marketing strategies in terms of environmental protection, but are actually leaning toward modern-oriented lifestyles and accessibility. Thus, it is more well-being marketing rather than green marketing. To pursue true green marketing despite the limits of newspaper advertisements, it is necessary to present products and pricing strategies that represent sustainable.

Complex Modulus of Alumina Green Tapes Measured by Micro Fourier Rheometer (Micro Fourier Rheometer에 의한 알루미나 그린 테이프의 Complex Modulus 측정)

  • ;;;;Michael V. Swain;Bruno Pfister
    • Journal of the Korean Ceramic Society
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    • v.36 no.2
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    • pp.122-129
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    • 1999
  • Alumina tapes, having various weight ratios of alumina powder/(alumina+binder+plasticizer), X, and binder / (binder+plsticizer), Y, were prepared and their complex modulus was measured using Micro Fourier Rheometer. As the X and Y ratios increased, Transfer function(TF) magnitude and Transfer function (TF) phase increased and decreased, respectively, indicating that the elastic modulus of the tapes depends on the weight ratios. The temperature dependence of the viscosity of the tapes was visualized by the decreased TF magnitude and the increased TF phase. The Y ratio dependence of the complex modulus related to the glass transition temperature of the tapes and the moduls change by the Y ratio was higher than that by the X ratio within the comperature of the tapes and the modulus changes by the Y ratio was higher than that by the X ratio within the composition range, investigated in the present study. The measurement of the complex modulus of the alumina tapes suggested that the TF phase should be higher that 17$^{\circ}$for the tapes to be utilized for 3-dimensional shaping.

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GREEN'S ADDITIVE COMPLEMENT PROBLEM FOR k-TH POWERS

  • Ding, Yuchen;Wang, Li-Yuan
    • Journal of the Korean Mathematical Society
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    • v.59 no.2
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    • pp.299-309
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    • 2022
  • Let k ⩾ 2 be an integer, Sk = {1k, 2k, 3k, …} and B = {b1, b2, b3, …} be an additive complement of Sk, which means all sufficiently large integers can be written as the sum of an element of Sk and an element of B. In this paper we prove that $${{\lim}\;{\sup}}\limits_{n{\rightarrow}{\infty}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^{\frac{k}{k-1}}{\Gamma}(1+{\frac{1}{k}})^{\frac{k}{k-1}}n^{\frac{k}{k-1}}-b_n}{n}}\;{\geqslant}\;{\frac{k}{2(k-1)}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^2}{{\Gamma}(2-{\frac{2}{k}})}},$$ where 𝚪(·) is Euler's Gamma function.