• Title/Summary/Keyword: polynomial functions

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Buckling of thick deep laminated composite shell of revolution under follower forces

  • Khayat, Majid;Poorveis, Davood;Moradi, Shapour;Hemmati, Mona
    • Structural Engineering and Mechanics
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    • v.58 no.1
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    • pp.59-91
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    • 2016
  • Laminated composite shells are commonly used in various engineering applications including aerospace and marine structures. In this paper, using semi-analytical finite strip method, the buckling behavior of laminated composite deep as well as thick shells of revolution under follower forces which remain normal to the shell is investigated. The stiffness caused by pressure is calculated for the follower forces subjected to external fibers in thick shells. The shell is divided into several closed strips with alignment of their nodal lines in the circumferential direction. The governing equations are derived based on first-order shear deformation theory which accounts for through thickness-shear flexibility. Displacements and rotations in the middle surface of shell are approximated by combining polynomial functions in the meridional direction as well as truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix which accounts for variation of loads direction will be derived for each strip of the shell. Assembling of these matrices results in global load stiffness matrix which may be un-symmetric. Upon forming linear elastic stiffness matrix called constitutive stiffness matrix, geometric stiffness matrix and load stiffness matrix, the required elements for the second step analysis which is an eigenvalue problem are provided. In this study, different parameter effects are investigated including shell geometry, material properties, and different boundary conditions. Afterwards, the outcomes are compared with other researches. By considering the results of this article, it can be concluded that the deformation-dependent pressure assumption can entail to decrease the calculated buckling load in shells. This characteristic is studied for different examples.

Design of Optimized Pattern Recognizer by Means of Fuzzy Neural Networks Based on Individual Input Space (개별 입력 공간 기반 퍼지 뉴럴 네트워크에 의한 최적화된 패턴 인식기 설계)

  • Park, Keon-Jun;Kim, Yong-Kab;Kim, Byun-Gon;Hoang, Geun-Chang
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.13 no.2
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    • pp.181-189
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    • 2013
  • In this paper, we introduce the fuzzy neural network based on the individual input space to design the pattern recognizer. The proposed networks configure the network by individually dividing each input space. The premise part of the networks is independently composed of the fuzzy partition of individual input spaces and the consequence part of the networks is represented by polynomial functions. The learning of fuzzy neural networks is realized by adjusting connection weights of the neurons in the consequent part of the fuzzy rules and it follows a back-propagation algorithm. In addition, in order to optimize the parameters of the proposed network, we use real-coded genetic algorithms. Finally, we design the optimized pattern recognizer using the experimental data for pattern recognition.

Intrinsically Extended Moving Least Squares Finite Difference Method for Potential Problems with Interfacial Boundary (계면경계를 갖는 포텐셜 문제 해석을 위한 내적확장된 이동최소제곱 유한차분법)

  • Yoon, Young-Cheol;Lee, Sang-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.22 no.5
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    • pp.411-420
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    • 2009
  • This study presents an extended finite difference method based on moving least squares(MLS) method for solving potential problems with interfacial boundary. The approximation constructed from the MLS Taylor polynomial is modified by inserting of wedge functions for the interface modeling. Governing equations are node-wisely discretized without involving element or grid; immersion of interfacial condition into the approximation circumvents numerical difficulties owing to geometrical modeling of interface. Interface modeling introduces no additional unknowns in the system of equations but makes the system overdetermined. So, the numbers of unknowns and equations are equalized by the symmetrization of the stiffness matrix. Increase in computational effort is the trade-off for ease of interface modeling. Numerical results clearly show that the developed numerical scheme sharply describes the wedge behavior as well as jumps and efficiently and accurately solves potential problems with interface.

Numerical Evaluation of Fundamental Finite Element Models in Bar and Beam Structures (Bar와 Beam 구조물의 기본적인 유한요소 모델의 수치해석)

  • Ryu, Yong-Hee;Ju, Bu-Seog;Jung, Woo-Young;Limkatanyu, Suchart
    • Journal of the Korean Society for Advanced Composite Structures
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    • v.4 no.1
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    • pp.1-8
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    • 2013
  • The finite element analysis (FEA) is a numerical technique to find solutions of field problems. A field problem is approximated by differential equations or integral expressions. In a finite element, the field quantity is allowed to have a simple spatial variation in terms of linear or polynomial functions. This paper represents a review and an accuracy-study of the finite element method comparing the FEA results with the exact solution. The exact solutions were calculated by solid mechanics and FEA using matrix stiffness method. For this study, simple bar and cantilever models were considered to evaluate four types of basic elements - constant strain triangle (CST), linear strain triangle (LST), bi-linear-rectangle(Q4),and quadratic-rectangle(Q8). The bar model was subjected to uniaxial loading whereas in case of the cantilever model moment loading was used. In the uniaxial loading case, all basic element results of the displacement and stress in x-direction agreed well with the exact solutions. In the moment loading case, the displacement in y-direction using LST and Q8 elements were acceptable compared to the exact solution, but CST and Q4 elements had to be improved by the mesh refinement.

A Study on the Effect of Cohesive Laws on Finite Element Analysis of Crack Propagation Using Cohesive Elements (응집 요소를 사용한 균열 진전 유한요소 해석에서 응집 법칙의 영향에 대한 연구)

  • Seo, Hyeong-Seok;Baek, Hyung-Chan;Kim, Hyun-Gyu
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.38 no.4
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    • pp.401-407
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    • 2014
  • In this paper, the effect of cohesive laws on the finite element analysis of crack propagation using cohesive elements is investigated through three-point bending and double cantilever beam problems. The cohesive elements are implemented into ABAQUS/Standard user subroutines(UEL), and the shape of cohesive law is varied by changing parameters in polynomial functions of cohesive traction-separation relations. In particular, crack propagation behaviors are studied by comparing load-displacement curves of the analysis models which have different shapes of cohesive laws with the same values of fracture energy and cohesive strength. Furthermore, the influence of the element size on crack propagation is discussed in this study.

New Method for Station Keeping of Geostationary Spacecraft Using Relative Orbital Motion and Optimization Technique (상대 운동과 최적화 기법을 이용한 정지궤도 위치유지에 관한 연구)

  • Jung, Ok-Chul;No, Tae-Soo;Lee, Sang-Cherl;Yang, Koon-Ho;Choi, Seong-Bong
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.1
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    • pp.39-47
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    • 2005
  • In this paper, a method of station keeping strategy using relative orbital motion and numerical optimization technique is presented for geostationary spacecraft. Relative position vector with respect to an ideal geostationary orbit is generated using high precision orbit propagation, and compressed in terms of polynomial and trigonometric function. Then this relative orbit model is combined with optimization scheme to propose a very efficient and flexible method of station keeping planning. Proper selection of objective and constraint functions for optimization can yield a variety of station keeping methods improved over the classical ones. Results from the nonlinear simulation have been shown to support such concept.

The design of phase error detector based on delayed n-tap rising edge clock:It's DP-PLL system application (지연된 n-탭 상승 에지 클럭을 이용한 위상 오차 검출기의 설계와 DP-PLL에의 적용)

  • 박군종;구광일;윤정현;윤대희;차일환
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.23 no.4
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    • pp.1100-1112
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    • 1998
  • In this paper, a novel method of minimizing the phase error is proposed. A DP-PLL system using this method is implemented and its performacnce is investigated, too. The DP-PLL system detects the phase error between reference clock and locally generated system clock. The phase difference is then reported as a PEV(Phase Error Variation), which is propoced from the delayted n-tap rising dege clock circuit with 5ns resolution in the phase detector. The algorithm is used to track the optimal DAC coefficients, which are adjusted from sample to sample in such a way as to minimize the PEV. The proposed method is found to have remarkable good potential for fast and accurate phase error tracking characteristic. The algorithm shows good performance to supress the low frequency jitter.-ending points, we design new basis functions based on the Legendre polynomial and then transform the error signals with them. When applied to synthetic images such as circles, ellipses and etc., the proposed method provides, in overall, outstanding results in respect to the transform coding gain compared with DCT and DST. And in the case when applied to natural images, the proposed method gives better image quality over DCT and comparable results with DST.

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Nonlinear Inference Using Fuzzy Cluster (퍼지 클러스터를 이용한 비선형 추론)

  • Park, Keon-Jung;Lee, Dong-Yoon
    • Journal of Digital Convergence
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    • v.14 no.1
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    • pp.203-209
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    • 2016
  • In this paper, we introduce a fuzzy inference systems for nonlinear inference using fuzzy cluster. Typically, the generation of fuzzy rules for nonlinear inference causes the problem that the number of fuzzy rules increases exponentially if the input vectors increase. To handle this problem, the fuzzy rules of fuzzy model are designed by dividing the input vector space in the scatter form using fuzzy clustering algorithm which expresses fuzzy cluster. From this method, complex nonlinear process can be modeled. The premise part of the fuzzy rules is determined by means of FCM clustering algorithm with fuzzy clusters. The consequence part of the fuzzy rules have four kinds of polynomial functions and the coefficient parameters of each rule are estimated by using the standard least-squares method. And we use the data widely used in nonlinear process for the performance and the nonlinear characteristics of the nonlinear process. Experimental results show that the non-linear inference is possible.

Identification Methodology of FCM-based Fuzzy Model Using Particle Swarm Optimization (입자 군집 최적화를 이용한 FCM 기반 퍼지 모델의 동정 방법론)

  • Oh, Sung-Kwun;Kim, Wook-Dong;Park, Ho-Sung;Son, Myung-Hee
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.60 no.1
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    • pp.184-192
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    • 2011
  • In this study, we introduce a identification methodology for FCM-based fuzzy model. The two underlying design mechanisms of such networks involve Fuzzy C-Means (FCM) clustering method and Particle Swarm Optimization(PSO). The proposed algorithm is based on FCM clustering method for efficient processing of data and the optimization of model was carried out using PSO. The premise part of fuzzy rules does not construct as any fixed membership functions such as triangular, gaussian, ellipsoidal because we build up the premise part of fuzzy rules using FCM. As a result, the proposed model can lead to the compact architecture of network. In this study, as the consequence part of fuzzy rules, we are able to use four types of polynomials such as simplified, linear, quadratic, modified quadratic. In addition, a Weighted Least Square Estimation to estimate the coefficients of polynomials, which are the consequent parts of fuzzy model, can decouple each fuzzy rule from the other fuzzy rules. Therefore, a local learning capability and an interpretability of the proposed fuzzy model are improved. Also, the parameters of the proposed fuzzy model such as a fuzzification coefficient of FCM clustering, the number of clusters of FCM clustering, and the polynomial type of the consequent part of fuzzy rules are adjusted using PSO. The proposed model is illustrated with the use of Automobile Miles per Gallon(MPG) and Boston housing called Machine Learning dataset. A comparative analysis reveals that the proposed FCM-based fuzzy model exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature.

Fuzzy Inference Systems Based on FCM Clustering Algorithm for Nonlinear Process (비선형 공정을 위한 FCM 클러스터링 알고리즘 기반 퍼지 추론 시스템)

  • Park, Keon-Jun;Kang, Hyung-Kil;Kim, Yong-Kab
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.5 no.4
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    • pp.224-231
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    • 2012
  • In this paper, we introduce a fuzzy inference systems based on fuzzy c-means clustering algorithm for fuzzy modeling of nonlinear process. Typically, the generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, the fuzzy rules of fuzzy model are generated by partitioning the input space in the scatter form using FCM clustering algorithm. The premise parameters of the fuzzy rules are determined by membership matrix by means of FCM clustering algorithm. The consequence part of the rules is expressed in the form of polynomial functions and the coefficient parameters of each rule are determined by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process.