• Title/Summary/Keyword: Secant Method

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Nonlinear Analysis of Space Trusses Using the Combined Arc-Length Method (복합 호장법을 이용한 공간 트러스의 비선형 해석)

  • 석창목;권영환
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.14 no.3
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    • pp.361-369
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    • 2001
  • This paper deals with numerical efficiency of nonlinear solution technique for space trusses. It will propose the combined Arc-length method to trace structural behavior after reaching buckling load as opposed to the current Arch-length method. The combined Arc-length method uses the current stiffness parameter as a control variable. It uses Secant-Newton method in stable path and applies Arc-length method in unstable path. To evaluate efficiency of solution technique, the accuracy of solution, convergence, and computing time concerning illustrative numerical examples are compared with the current Arc-length method. It show that the combined Arc-length method, as proposed in this paper, is superior to the current Arc-length method in numerical nonlinear analysis.

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Nonlinear finite element model of the beam-to-column connection for precast concrete frames with high ratio of the continuity tie bars

  • Sergio A. Coelho;Sergio A. Coelho
    • Computers and Concrete
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    • v.31 no.1
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    • pp.53-69
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    • 2023
  • The rotational stiffness of a semi-rigid beam-to-column connection plays an important role in the reduction of the second-order effects in the precast concrete skeletal frames. The aim of this study is to present a detailed nonlinear finite element study to reproduce the experimental response of a semi-rigid precast beam-to-column connection composed by corbel, dowel bar and continuity tie bars available in the literature. A parametric study was carried using four arrangements of the reinforcing tie bars in the connection, including high ratio of the continuity tie bars passing around the column in the cast-in-place concrete. The results from the parametric study were compared to analytical equations proposed to evaluate the secant rotational stiffness of beam-to-column connections. The good agreement with the experimental results was obtained, demonstrating that the finite element model can accurately predict the structural behaviour of the beam-to-column connection despite its complex geometric configuration. The secant rotational stiffness of the connection was good evaluated by the analytical model available in the literature for ratio of the continuity tie bars of up to 0.69%. Precast beam-to-column connection with a ratio of the continuity tie bars higher than 1.4% had the secant stiffness overestimated. Therefore, an adjustment coefficient for the effective depth of the crack at the end of the beam was proposed for the analytical model, which is a function of the ratio of the continuity tie bars.

Separations and Feature Extractions for Image Signals Using Independent Component Analysis Based on Neural Networks of Efficient Learning Rule (효율적인 학습규칙의 신경망 기반 독립성분분석을 이용한 영상신호의 분리 및 특징추출)

  • Cho, Yong-Hyun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.13 no.2
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    • pp.200-208
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    • 2003
  • This paper proposes a separation and feature extraction of image signals using the independent component analysis(ICA) based on neural networks of efficient learning rule. The proposed learning rule is a hybrid fixed-point(FP) algorithm based on secant method and momentum. Secant method is applied to improve the performance by simplifying the 1st-order derivative computation for optimizing the objective function, which is to minimize the mutual informations of the independent components. The momentum is applied for high-speed convergence by restraining the oscillation in the process of converging to the optimal solution. The proposed algorithm has been applied to the composite images generated by random mixing matrix from the 10 images of $512\times512$-pixel. The simulation results show that the proposed algorithm has better performances of the separation speed and rate than those using the FP algorithm based on Newton and secant method. The proposed algorithm has been also applied to extract the features using a 3 set of 10,000 image patches from the 10 fingerprints of $256\times256$-pixel and the front and the rear paper money of $480\times225$-pixel, respectively, The simulation results show that the proposed algorithm has also better extraction speed than those using the another methods. Especially, the 160 basis vectors(features) of $16\times16$-pixel show the local features which have the characteristics of spatial frequency and oriented edges in the images.

A Steady Method of Damping Coefficient Prediction for Axisymmetric Projectiles (축대칭 발사체의 감쇠계수 계산을 위한 정상 해법)

  • Park, Soo-Hyung;Kwon, Jang-Hyuk;Yu, Yung-Hoon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.34 no.11
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    • pp.1-8
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    • 2006
  • A steady prediction method is presented to compute dynamic damping coefficients for axisymmetric projectiles. Viscous flow analysis is essential to the steady method using a zero-spin coning motion in the inertial coordinate frame. The present method is applied to compute the pitching moment and the pitch-damping moment coefficients for the Army-Navy Spinning Rocket. The results are in good agreement with the parabolized Navier-Stokes data, range data, and unsteady prediction data. Predictions for Secant-Ogive-Cylinder configurations are performed to investigate effects of afterbody geometries. To investigate the geometrical effect and flow physics, the longitudinal developments of the coefficients are examined in detail.

Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory

  • Abdulrazzaq, Mohammed Abdulraoof;Fenjan, Raad M.;Ahmed, Ridha A.;Faleh, Nadhim M.
    • Steel and Composite Structures
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    • v.35 no.1
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    • pp.147-157
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    • 2020
  • In the present research, thermo-elastic buckling of small scale functionally graded material (FGM) nano-size plates with clamped edge conditions rested on an elastic substrate exposed to uniformly, linearly and non-linearly temperature distributions has been investigated employing a secant function based refined theory. Material properties of the FGM nano-size plate have exponential gradation across the plate thickness. Using Hamilton's rule and non-local elasticity of Eringen, the non-local governing equations have been stablished in the context of refined four-unknown plate theory and then solved via an analytical method which captures clamped boundary conditions. Buckling results are provided to show the effects of different thermal loadings, non-locality, gradient index, shear deformation, aspect and length-to-thickness ratios on critical buckling temperature of clamped exponential graded nano-size plates.

Single piles under cyclic lateral loads - Full scale tests and numerical modelling

  • Hocine Haouari;Ali Bouafia
    • Geomechanics and Engineering
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    • v.32 no.1
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    • pp.21-34
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    • 2023
  • In order to analyze the effect of the cyclic lateral loading on the response of a pile-soil system, a full-scale single steel pile was subjected to one-way cyclic loading. The test pile was driven into a bi-layered soil consisting of a normally consolidated saturated clay overlying a silty sandy layer, the site being submerged by water up to one meter above the mudline in order to reproduce the conditions of an offshore pile foundation. The aim of this paper is to present the main results of interpretation of the cyclic lateral tests in terms of pile deflections, bending moment, and cyclic P-Y curves. From these latter an absolute secant reaction modulus EAS,N was derived and a simple calculation model of the test single pile is proposed based on this modulus. Two applications of the proposed model are carried out, one with a 2D finite element modelling, and the second with a load transfer curves-based method.

A Study on Improvement of Dimensional Accuracy in 2-axis Bending for Automotive Blow Motor Case (차량용 블로우 모터 케이스 2축 굽힘 공정의 치수 정밀도 향상에 관한 연구)

  • Kwon, Il-Keun;Kim, Gug-Yong;Park, Jun-Woo
    • Journal of the Korean Society of Industry Convergence
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    • v.21 no.6
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    • pp.419-427
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    • 2018
  • In case high strength steels are applied for press-formed automotive parts, it is very difficult to secure forming accuracy due to large springback compared to moderate strength steels. In this study, a repetitive step-wise forming analyses based on secant method was proposed as the die design method for mandrel(bending tool) for the 2-axis bending equipments. A bending die with circular mandrel was designed for the DP780 blow motor case of which diameter and thickness are 70.8mm and 2.0mm respectively. Forming tests were performed to verify the validity of established die design and the results were compared with that of conventional HGI(Hot galvanized iron steel) blow motor case. For additional improvement in forming accuracy, an elliptical mandrel was proposed and its validity was verified using forming analyses based on secant method.

아르스 마그나와 프린키피아에 나오는 수치해석적 기법

  • 이무현
    • Journal for History of Mathematics
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    • v.15 no.3
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    • pp.25-34
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    • 2002
  • This paper explains methods of numerical analysis which appear on Cardano's Ars Magna and Newton's Principia. Cardano's method is secant method, but its actual al]plication is severely limited by technical difficulties. Newton's method is what nowadays called Newton-Raphson's method. But mysteriously, Newton's explanation had been forgotten for two hundred years, until Adams rediscovered it. Newton had even explained finding the root using the second degree Taylor's polynomial, which shows Newton's greatness.

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Nonlinear analyses of steel beams and arches using virtual unit moments and effective rigidity

  • Koubova, Lenka;Janas, Petr;Markopoulos, Alexandros;Krejsa, Martin
    • Steel and Composite Structures
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    • v.33 no.5
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    • pp.755-765
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    • 2019
  • This study examined geometric and physical nonlinear analyses of beams and arches specifically from rolled profiles used in mining and underground constructions. These profiles possess the ability to create plastic hinges owing to their robustness. It was assumed that displacements in beams and arches fabricated from these profiles were comparable with the size of the structure. It also considered changes in the shape of a rod cross-section and the nonlinearities of the structure. The analyses were based on virtual unit moments, effective flexural rigidity of used open sections, and a secant method. The use of the approach led to a solution for the "after-critical" condition in which deformation increased with decreases in loads. The solution was derived for static determinate beams and static indeterminate arches. The results were compared with results obtained in other experimental tests and methods.

Elastic stiffness of perfobond connections in composite structures

  • Qin, Xi;Yang, Guotao
    • Steel and Composite Structures
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    • v.42 no.2
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    • pp.221-241
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    • 2022
  • Perfobond rib connectors are widely used in composite structures to achieve the composite action between the steel and the concrete, and empirical expressions for their strength and secant stiffness have been obtained by numerical simulations or push-out tests. Since perfobond connections are generally in an elastic state in the service process and the structural analysis are always based on the elastic properties of the members, the secant stiffness is not applicable for the normal structural analysis. However, the tangent stiffness of perfobond connections has not been introduced in previous studies. Moreover, the perfobond connections are bearing tension and shear force simultaneously when the composite beams subjected to torque or local loads, but the current studies fail to arrive at the elastic stiffness considering the combined effects. To resolve these discrepancies, this paper investigates the initial elastic stiffness of perfobond connections under combined forces. The calculation method for the elastic stiffness of perfobond connections is analyzed, and the contributions of the perfobond rib, the perforating rebar and the concrete dowel are investigated. A finite element method was verified with a high value of correlation for the test results. Afterwards, parametric studies are carried out using the reliable finite element analysis to explore the trends of several factors. Empirical equations for predicting the initial elastic stiffness of perfobond connections are proposed by the numerical regression of the data extracted by parametric studies. The equations agree well with finite element analysis and test results, which indicates that the proposed empirical equations reflect a high accuracy for predicting the initial elastic stiffness of perfobond connections.