• Title, Summary, Keyword: Analytical method

### Augmented Displacement Load Method for Nonlinear Semi-analytical Design Sensitivity Analysis (준해석적 비선형 설계민감도를 위한 개선된 변위하중법)

• Lee, Min-Uk;Yoo, Jung-Hun;Lee, Tae-Hee
• Proceedings of the KSME Conference
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• pp.492-497
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• 2004
• Three methods for design sensitivity such as numerical differentiation, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

### Displacement-Load Method for Semi-Analytical Design Sensitivity Analysis (준해석 설계민감도를 위한 변위하중법)

• Yoo Jung Hun;Kim Heung Seok;Lee Tae Hee
• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.10
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• pp.1590-1597
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• 2004
• Three methods of design sensitivity analysis for structures such as numerical method, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis can provide very exact result, it is difficult to implement into practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable fur most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate in nonlinear design sensitivity analysis because its computational cost depends on the number of design variables and large numerical errors can be included. Thus the semi-analytical method is more suitable for complicated design problems. Moreover, semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure fur the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and the computational technique is proposed for evaluating the partial differentiation of internal nodal force, so called pseudo-load. Numerical examples coupled with commercial finite element package are shown to verify usefulness of proposed semi-analytical sensitivity analysis procedure and computational technique for pseudo-load.

### Development of new integrated particle tracking techniques combining the numerical method, semi-analytical method, and analytical method (수치, 해석적, 준 해석적 및 해석적 방법을 통합한 새로운 입자추적기술 개발)

• Suk, Hee-Jun
• Journal of Soil and Groundwater Environment
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• v.13 no.6
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• pp.50-61
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• 2008
• In this study, new integrated particle tracking algorithm was developed to reduce the inherent problem of Eulerian- Lagrangian method, or adverse effect of particle tracking error on mass balance error. The new integrated particle tracking algorithm includes numerical method, semi-analytical method, and analytical method which consider both temporal and spatial changes of velocity field during time step. Detail of mathematical derivations is well illustrated and four examples are made to verify through the comparison of the new integrated particle tracking with analytical solution or Runge-Kutta method. Additionally, It was shown that the there is better superiority of the new integrated particle tracking algorithm over other existing particle tracking method such as Lu's method.

### A new analysis on timing jitters in APD receivers of optical communication systems when considering intersymbol interferences (APD를 사용하는 광통신 시스템 수신기에서 심벌간 간섭을 고려할 경우 타이밍 지터에 대한 새로운 해석)

• 신요안;은수정;김부균
• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.3
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• pp.539-546
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• 1997
• In this paper, we proposed a new mehtod to analyze the performance degradation by timing jitters in the APD (avalanche photodiode) receivers of intensity modulation/direct detection digital optical communication systems where raised cosine pulse-shaping filters are used to reduce the effect of noise while minimizing intersymbol interferences. The proposed analytical method is an extension of an analytical method we have already developed for pin diode receivers, and incorporates the effects of APD's multiplication factor and resulting shot noise. Using the proposed analytical method, we derive an approximated power penalty due to timing jitters based on an assumption of Gaussian distribution for timing jitters, and compare with that of the conventional analytical method. The results obtained from the proposed analytical method show that conventional analytical methods underestimate the influence of timing jitters on the reciver performance. The results also show that APD's multiplication factor which optimizes receiver sensitivity is smaller than that obtained by the conventional analytical method.

### Accurate buckling analysis of rectangular thin plates by double finite sine integral transform method

• Ullah, Salamat;Zhang, Jinghui;Zhong, Yang
• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.491-502
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• 2019
• This paper explores the analytical buckling solution of rectangular thin plates by the finite integral transform method. Although several analytical and numerical developments have been made, a benchmark analytical solution is still very few due to the mathematical complexity of solving high order partial differential equations. In solution procedure, the governing high order partial differential equation with specified boundary conditions is converted into a system of linear algebraic equations and the analytical solution is obtained classically. The primary advantage of the present method is its simplicity and generality and does not need to pre-determine the deflection function which makes the solving procedure much reasonable. Another advantage of the method is that the analytical solutions obtained converge rapidly due to utilization of the sum functions. The application of the method is extensive and can also handle moderately thick and thick elastic plates as well as bending and vibration problems. The present results are validated by extensive numerical comparison with the FEA using (ABAQUS) software and the existing analytical solutions which show satisfactory agreement.

### Theoretical analysis of Y-shape bridge and application

• Lu, Peng-Zhen;Zhang, Jun-Ping;Zhao, Ren-Da;Huang, Hai-Yun
• Structural Engineering and Mechanics
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• v.31 no.2
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• pp.137-152
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• 2009
• Mechanic behavior of Y-shape thin-walled box girder bridge structure is complex, so one can not exactly hold the mechanical behavior of the Y-shape thin-walled box girder bridge structure through general calculation theory and analytical method. To hold the mechanical behavior better, based on elementary beam theory, by increasing the degree of freedom analytical method, taking account of restrained torsiondistortion angledistortion warp and shearing lag effect at the same time, authors obtain a thin-walled box beam analytical element of 10 degrees of freedom of every node, derive stiffness matrix of the element, and code a finite element procedure. In addition, authors combine the obtained procedure with spatial grillage analytical method, meanwhile, they build a new analytical method that is the spatial thin-walled box girder element grillage analysis method. In order to validate the precision of the obtained analysis method, authors analyze a type Y-shape thin-walled box girder bridge structure according to the elementary beam theory analytical method, the shell theory analytical method and the spatial thin-walled box girder element grillage analysis method respectively. At last, authors test a type Y-shape thin-walled box girder bridge structure. Comparisons of the results of theory analysis with the experimental text show that the spatial thin-walled box girder element grillage analysis method is simple and exact. The research results are helpful for the knowledge of the mechanics property of these Y-shape thin-walled box girder bridge structures.

### Consistent Displacement Load Method for Nonlinear Semi-Analytical Design Sensitivity Analysis (준해석적 비선형 설계민감도를 위한 보정변위하중법)

• Lee, Min-Uk;Yoo, Jung-Hun;Lee, Tae-Hee
• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9
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• pp.1209-1216
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• 2005
• Three methods for design sensitivity such as numerical differentiation, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

### Eddy Current Loss Analysis of Slotless Double-sided Cored Type Permanent Magnet Generator by using Analytical Method (해석적 방법을 이용한 슬롯리스 양측식 코어드 타입 영구자석 발전기의 와전류 손실 해석)

• Jang, Gang-Hyeon;Jung, Kyoung-Hun;Hong, Keyyong;Kim, Kyong-Hwan;Choi, Jang-Young
• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.10
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• pp.1639-1647
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• 2016
• This paper deals with eddy current loss analysis of Slotless Double sided Cored type permanent magnet linear generator by using analytical method, space harmonic method. In order to calculate eddy current, this paper derives analytical solution by the Maxwell equation, magnetic vector potential, Faraday's law and a two-dimensional(2-D) cartesian coordinate system. First, we derived the armature reaction field distribution produced by armature wingding current. Second, by using derived armature reaction field solution, the analytical solution for eddy current density distribution are also obtained. Finally, the analytical solution for eddy current loss induced in permanent magnets(PMs) are derived by using equivalent, electrical resistance calculated from PMs volume and eddy current density distribution solution. The analytical result from space harmonic method are validated extensively by comparing with finite element method(FEM).

### Analytical approximate solution for Initial post-buckling behavior of pipes in oil and gas wells

• Yu, Yongping;Sun, Youhong;Han, Yucen
• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012
• This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

### Nonlinear vibration analysis of a type of tapered cantilever beams by using an analytical approximate method

• Sun, Weipeng;Sun, Youhong;Yu, Yongping;Zheng, Shaopeng
• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.1-14
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• 2016
• In this paper, an alternative analytical method is presented to evaluate the nonlinear vibration behavior of single and double tapered cantilever beams. The admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Based on the Lagrange method and the Newton Harmonic Balance (NHB) method, analytical approximate solutions in closed and explicit form are obtained. These approximate solutions show excellent agreement with those of numeric method for small as well as large amplitude. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large amplitude vibration response of tapered beams.