• Title/Summary/Keyword: non-linear problem

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Numerical solution of beam equation using neural networks and evolutionary optimization tools

  • Babaei, Mehdi;Atasoy, Arman;Hajirasouliha, Iman;Mollaei, Somayeh;Jalilkhani, Maysam
    • Advances in Computational Design
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    • v.7 no.1
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    • pp.1-17
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    • 2022
  • In this study, a new strategy is presented to transmit the fundamental elastic beam problem into the modern optimization platform and solve it by using artificial intelligence (AI) tools. As a practical example, deflection of Euler-Bernoulli beam is mathematically formulated by 2nd-order ordinary differential equations (ODEs) in accordance to the classical beam theory. This fundamental engineer problem is then transmitted from classic formulation to its artificial-intelligence presentation where the behavior of the beam is simulated by using neural networks (NNs). The supervised training strategy is employed in the developed NNs implemented in the heuristic optimization algorithms as the fitness function. Different evolutionary optimization tools such as genetic algorithm (GA) and particle swarm optimization (PSO) are used to solve this non-linear optimization problem. The step-by-step procedure of the proposed method is presented in the form of a practical flowchart. The results indicate that the proposed method of using AI toolsin solving beam ODEs can efficiently lead to accurate solutions with low computational costs, and should prove useful to solve more complex practical applications.

The Selection of Measurement Positions for BEM Based NAH Using a Non-conformal Hologram to Reduce the Reconstruction Error

  • Oey, Agustinus;Ih, Jeong-Guon
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.11a
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    • pp.1018-1021
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    • 2007
  • This paper explores the use of BEM based NAH to reconstruct the surface vibration of a plate in a rectangular finite cavity, in which the distances between sensors and the nearest points on the source surface are not equal. In such circumstances, different degree of information on propagating and non-propagating wave components will be detected by sensors at different positions, as well as the influence of measurement noise will vary significantly from the nearest points of measurement to the farthest ones. On the other hand, the condition number of the vibro-acoustic transfer function matrix relating normal surface velocities and field pressures will becomes high, numerically indicating an increase of linear dependency between rows of transfer function matrix. The combination of poor measurement and high condition number will result inaccurate reconstruction. Therefore, one approach to be investigated in this work is to select the measurement positions in such ways that reduce measurement redundancy, as it indicated by the condition number. The improvement is found to be significant in the numerical simulations utilizing two different criterions, spanning from over-determined to under-determined cases, and in the validation experiment.

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CO-CLUSTER HOMOTOPY QUEUING MODEL IN NONLINEAR ALGEBRAIC TOPOLOGICAL STRUCTURE FOR IMPROVING POISON DISTRIBUTION NETWORK COMMUNICATION

  • V. RAJESWARI;T. NITHIYA
    • Journal of applied mathematics & informatics
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    • v.41 no.4
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    • pp.861-868
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    • 2023
  • Nonlinear network creates complex homotopy structural communication in wireless network medium because of complex distribution approach. Due to this multicast topological connection structure, the queuing probability was non regular principles to create routing structures. To resolve this problem, we propose a Co-cluster homotopy queuing model (Co-CHQT) for Nonlinear Algebraic Topological Structure (NLTS-) for improving poison distribution network communication. Initially this collects the routing propagation based on Nonlinear Distance Theory (NLDT) to estimate the nearest neighbor network nodes undernon linear at x(a,b)→ax2+bx2 = c. Then Quillen Network Decomposition Theorem (QNDT) was applied to sustain the non-regular routing propagation to create cluster path. Each cluster be form with co variance structure based on Two unicast 2(n+1)-Z2(n+1)-Z network. Based on the poison distribution theory X(a,b) ≠ µ(C), at number of distribution routing strategies weights are estimated based on node response rate. Deriving shorte;'l/st path from behavioral of the node response, Hilbert -Krylov subspace clustering estimates the Cluster Head (CH) to the routing head. This solves the approximation routing strategy from the nonlinear communication depending on Max- equivalence theory (Max-T). This proposed system improves communication to construction topological cluster based on optimized level to produce better performance in distance theory, throughput latency in non-variation delay tolerant.

Analysis of 2-D Potential Problem with L-shape Domain by p-Convergent Boundary Element Method (p-수렴 경계요소법에 의한 L-형 영역을 갖는 2차원 포텐셜 문제 해석)

  • Woo, Kwang-Sung;Jo, Jun-Hyung
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.22 no.1
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    • pp.117-124
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    • 2009
  • The p-convergent boundary element method has been proposed to analyze two-dimensional potential problem on the basis of high order Legendre shape functions that have different property comparing with the shape functions in conventional boundary element method. The location of nodes corresponding to high order shape function are not defined along the boundary, called by nodeless node, similar to the p-convergent finite element method. As the order of shape function increases, the collocation point method is used to solve linear simultaneous equations. The collocation patterns of p-convergent boundary element method consist of non-symmetric hierarchial or symmetric non-hierarchical. As the order of shape function increases, the number of collocation point increases. The singular integral that appears in p-convergent boundary element has been calculated by special numeric quadrature technique and semi-analytical integration technique. The L-shape domain problem including singularity in the vicinity of reentrant comer is analyzed and the numerical results show that the relative error is smaller than $10^{-2}%$ range as compared with other results in literatures. In case of same condition, the symmetric p-collocation point pattern shows high accuracy of solution.

Forced vibrations of an elastic rectangular plate supported by a unilateral two-parameter foundation via the Chebyshev polynomials expansion

  • Zekai Celep;Zeki Ozcan
    • Structural Engineering and Mechanics
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    • v.90 no.6
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    • pp.551-568
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    • 2024
  • The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

Rainfall-Runoff Analysis Utilizing Multiple Impulse Responses (복수의 임펄스 응답을 이용한 강우-유출 해석)

  • Yoo, Chul-Sang;Park, Joo-Young
    • Journal of the Korean Institute of Intelligent Systems
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    • v.16 no.5
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    • pp.537-543
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    • 2006
  • There have been many recent studies on the nonlinear rainfall-runoff modeling, where the use of neural networks is shown to be quite successful. Due to fundamental limitation of linear structures, employing linear models has often been considered inferior to the neural network approaches in this area. However, we believe that with an appropriate extension, the concept of linear impulse responses can be a viable tool since it enables us to understand underlying dynamics principles better. In this paper, we propose the use of multiple impulse responses for the problem of rainfall-runoff analysis. The proposed method is based on a simple and fixed strategy for switching among multiple linear impulse-response models, each of which satisfies the constraints of non-negativity and uni-modality. The computational analysis performed for a certain Korean hydrometeorologic data set showed that the proposed method can yield very meaningful results.

Acoustic Analysis of KSR-III Combustion Chamber with Various 5-Blade Baffles under Non-Reacting Condition (5-블레이드 배플이 설치된 로켓엔진 연소실에서의 상온음향 해석)

  • Kim, Hong-Jip;Kim, Seong-Ku;Sohn, Chae-Hoon
    • 한국연소학회:학술대회논문집
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    • 2003.05a
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    • pp.167-171
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    • 2003
  • Acoustic characteristics of baffled combustion chamber to elucidate suppressing effect of baffle on combustion instability are numerically investigated by linear acoustic analysis. A hub-blade baffle of 5 blades is selected as a candidate one and five variants of baffles with various configuration are designed. Resonant-frequency shift and damping factor are analyzed quantitatively as damping parameters. When the hub is located radially at the pressure node, the decrease of resonant frequency and increase of damping factor in 1R mode are dominant. But sub-1T mode is formed within hub, therefore, there would be a possibility of initiating 1T mode in unbaffled region, which would occur another problem. For smaller hub size, four kinds of axial baffle length is selected. As the axial baffle length increases, resonant frequency shift and increase of damping factor of transverse acoustic modes is obtained. Especially, two close acoustic modes such as 1L and 1T could be overlapped for a certain axial length, resulting in extreme increase of damping factor. The present study based on linear acoustic analysis is expected to be a useful confirming tool to predict acoustic field and design a passive control devices such as baffle and acoustic cavity.

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A Study on the improvement of reverberation characteristics using tapped and nested-allpass delay line (Tapped and nested-allpass delay line을 이용한 잔향특성 개선에 관한 연구)

  • Yoon, Jae-Yeun;Park, Jun-Sun;Jin, Yong-Ok
    • Journal of Broadcast Engineering
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    • v.12 no.1 s.34
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    • pp.28-40
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    • 2007
  • In this paper, we proposes an idea for improved sound characteristic which decreasing a problem in previous reverberation algorism structure. To later reflection sound, proposed new reverberation structure, using a lopped and nested all-pass delay line, and it is designed to improve an natural concert hall sound. In addition, In order to have best imaginary sound effect, we extracted the factors by controlling each delay line's delay time, and we realized a proposed new algorithm by using general-purpose DSP. Through several experimental cases, we observed better effect on improvement of linear flatten and reverberation density and decreasing about colorlessness and non-linear sound at previous proposed model about impulse input.

FACTORS AFFECTING PRODUCTIVITY ON DAIRY FARMS IN TROPICAL AND SUB-TROPICAL ENVIRONMENTS

  • Kerr, D.V.;Davison, T.M.;Cowan, R.T.;Chaseling, J.
    • Asian-Australasian Journal of Animal Sciences
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    • v.8 no.5
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    • pp.505-513
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    • 1995
  • The major factors affecting productivity on daily farms in Queensland, Australia, were determined using the stepwise linear regression approach. The data were obtained from a survey conducted on the total population of daily farms in Queensland in 1987. These data were divided into six major dailying regions. The technique was applied using 12 independent variables believed by a panel of experienced research and extension personnel to exert the most influence on milk production. The regression equations were all significant (p < 0.001) with the percentage coefficients of determination ranging from 62 to 76% for equations developed using' total farm milk: production as the dependent variable. Three of the variables affecting total farm milk: production were found to be common to all six regions. These were; the amount of supplementary energy fed, the area set aside to irrigate winter feed and the size of the area used for dailying. Higher production farms appeared to be more efficient in that they consistently produced milk production levels higher than those estimated from the regression equation for their region. Other methods of analysis including robust regression and non linear regression techniques were unsuccessful in overcoming this problem and allowing development of a model appropriate for farms at all levels of production.

Development of Geometrically Nonlinear Finite Element Analysis Examples for Computational Structural Analysis (전산구조해석을 위한 기하학적 비선형 유한요소해석 예제 개발)

  • Na, Won-Bae;Lee, Sun-Min
    • Journal of Fisheries and Marine Sciences Education
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    • v.24 no.5
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    • pp.699-711
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    • 2012
  • An undergraduate course named computational structural analysis becomes more significant in recent years because of its important role in industries and the recent innovation in computer technology. Typically, the course consists of introduction to finite element method, utilization of general purpose finite element software, and examples focusing on static and linear analyses on various structural members such as a beam, truss, frame, arch, and cable. However, in addition to the static and linear analyses, current industries ask graduates to acquire basic knowledge on structural dynamics and nonlinear analysis, which are not listed in the conventional syllabus of the computational structural analysis. Therefore, this study develops geometrically nonlinear examples, which can help students to easily capture the fundamental nonlinear theory, software manipulation, and problem solving skills. For the purpose, five different examples are found, developed for the analyses of cables and cable nets, which naturally have strong geometrical non-linearity. In the paper, these examples are presented, discussed, and finally compared for a better subject development.