• Title/Summary/Keyword: Functions of matrices

검색결과 180건 처리시간 0.024초

Stability Analysis of Shear-Flexible and Semi-Rigid Plane Frames (전단변형효과를 고려한 부분강절 평면뼈대구조의 안정성 해석)

  • Min, Byoung Cheol;Min, Dong Ju;Jung, Myung Rag;Kim, Moon Young
    • KSCE Journal of Civil and Environmental Engineering Research
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    • 제31권1A호
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    • pp.9-18
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    • 2011
  • Generally the connection of structural members is assumed as hinge, rigid and semi-rigid connections. The exact tangent stiffness matrix of a semi-rigid frame element is newly derived using the stability functions considering shear deformations. Also, linearized elastic- and geometric-stiffness matrices of shear deformable semi-rigid frame are newly proposed. For the exact stiffness matrix, an accurate displacement field is introduced by equilibrium equation for beam-column under the bending and the axial forces. Also, stability functions considering sway deformation and force-displacement relations with elastic rotational spring on ends are defined. In order to illustrate the accuracy of this study, various numerical examples are presented and compared with other researcher's results. Lastly, shear deformation and semi-rigid effects on buckling behaviors of structure are parametrically investigated.

Analysis of laminated composite plates based on different shear deformation plate theories

  • Tanzadeh, Hojat;Amoushahi, Hossein
    • Structural Engineering and Mechanics
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    • 제75권2호
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    • pp.247-269
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    • 2020
  • A finite strip formulation was developed for buckling and free vibration analysis of laminated composite plates based on different shear deformation plate theories. The different shear deformation theories such as Zigzag higher order, Refined Plate Theory (RPT) and other higher order plate theories by variation of transverse shear strains through plate thickness in the parabolic form, sine and exponential were adopted here. The two loaded opposite edges of the plate were assumed to be simply supported and remaining edges were assumed to have arbitrary boundary conditions. The polynomial shape functions are applied to assess the in-plane and out-of-plane deflection and rotation of the normal cross-section of plates in the transverse direction. The finite strip procedure based on the virtual work principle was applied to derive the stiffness, geometric and mass matrices. Numerical results were obtained based on various shear deformation plate theories to verify the proposed formulation. The effects of length to thickness ratios, modulus ratios, boundary conditions, the number of layers and fiber orientation of cross-ply and angle-ply laminates were determined. The additional results on the same effects in the interaction of biaxial in-plane loadings on the critical buckling load were determined as well.

Analytical p-version finite elements and application in analyses of structural collision protection

  • Zhu, B.;Chen, Y.M.;Leung, A.Y.T.
    • Structural Engineering and Mechanics
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    • 제23권5호
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    • pp.487-504
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    • 2006
  • Several new versatile two-dimensional p-version finite elements are developed. The element matrices are integrated analytically to guarantee the accuracy and monotonic convergence of the predicted solutions of the proposed p-version elements. The analysis results show that the convergence rate of the present elements is very fast with respect to the number of additional Fourier or polynomial terms in shape functions, and their solutions are much more accurate than those of the linear finite elements for the same number of degrees of freedom. Additionally, the new p-version plate elements without the reduced integration can overcome the shear locking problem over the conventional h-version elements. Using the proposed p-version elements with fast convergent characteristic, the elasto-plastic impact of the structure attached with the absorber is simulated. Good agreement between the simulated and experimental results verifies the present p-version finite elements for the analyses of structural dynamic responses and the structural elasto-plastic impact. Further, using the elasto-plastic impact model and the p-version finite element method, the absorber of the T structure on the Qiantang River is designed for its collision protection.

NUMERICAL METHODS FOR SOME NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS

  • El-Borai, Mahmoud M.;El-Nadi, Khairia El-Said;Mostafa, Osama L.;Ahmed, Hamdy M.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제9권1호
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    • pp.79-90
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    • 2005
  • In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,\;t)=f(x,\;t,\;u)dt\;+\;g(x,\;t,\;u)dW(t)\;+\;\sum\limits_{|q|\leq2m}\;A_q(x,\;t)D^qu(x,\;t)dt$$ where $0\;{\leq}\;t\;{\leq}\;T,\;x\;{\in}\;R^{\nu}$, ($R^{nu}$ is the $\nu$-dimensional Euclidean space). Here $u\;{\in}\;R^n$, W(t) is an n-dimensional Brownian motion, $$f\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^n,\;g\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^{n{\times}n},$$, and $$A_q\;:\;R^{\nu}\;{\times}\;[0,\;T]\;{\rightarrow}\;R^{n{\times}n}$$ where ($A_q,\;|\;q\;|{\leq}\;2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.

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Adaptive finite element wind analysis with mesh refinement and recovery

  • Choi, Chang-Koon;Yu, Won-Jin
    • Wind and Structures
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    • 제1권1호
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    • pp.111-125
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    • 1998
  • This paper deals with the development of variable-node element and its application to the adaptive h-version mesh refinement-recovery for the incompressible viscous flow analysis. The element which has variable mid-side nodes can be used in generating the transition zone between the refined and unrefined element and efficiently used for the construction of a refined mesh without generating distorted elements. A modified Guassian quadrature is needed to evaluate the element matrices due to the discontinuity of derivatives of the shape functions used for the element. The penalty function method which can reduce the number of the independent variables is adopted for the purpose of computational efficiency and the selective reduced integration is carried out for the convection and pressure terms to preserve the stability of solution. For the economical analysis of transient problems in which the locations to be refined are changed in accordance with the dynamic distribution of velocity gradient, not only the mesh refinement but also the mesh recovery is needed. The numerical examples show that the optimal mesh for the finite element analysis of a wind around the structures can be obtained automatically by the proposed scheme.

Extended Quasi Orthogonal Functions for 3G CDMA Systems (3G CDMA 시스템을 위한 확장 준직교 함수)

  • Lee Kwang-Jae;Moon Myung-Ryong;Hou Jia;Lee Moon-Ho
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • 제16권7호
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    • pp.697-708
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    • 2005
  • The forward link of the 3G CDMA system may become limited under the increasing of the number of users. The conventional channelization code, Walsh code, has not enough sizes f3r much possible users, therefore, the quasi orthogonal function(QOF), which process optimal crosscorrelation with Walsh code, is considered. In this paper, we investigate quasi orthogonal function on Jacket matrices, which can lead lower correlations values and better performance in 3G CDMA system. Moreover, to simplify the detector and improve the BER performance, a novel detection for QOF CDMA system is proposed. Finally, the simple recursive generation of the bent sequences for QOF mask function is discussed.

Thermoviscoelastic Stress Analysis by the Finite Element Method (유한요소법에 의한 열점탄성 응력해석)

  • Sim, Woo-JIn;Park, In-Kyu
    • Transactions of the Korean Society of Mechanical Engineers A
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    • 제20권7호
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    • pp.2148-2158
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    • 1996
  • Uncoupled, quasi-static and linear thermoviscoelastic problems are analyzed in time domain by the finite element approximation which is developed using the principle of virtual work and viscoelasticity matrices instead of shear and bulk relaxation functions as in usual formulations. The material is assumed to be isotropic, homegeneous and thermorheologically simple, which means that the temperature-time equivalence postulate is effective. The stress-strain laws are expressed by relaxation-type hereditary integrals. In spatial and time discritizations, isoparametric quadratic quadrilateral finite elements and linear time variations are adopted. For explicit derivations, the viscoelastic material is assumed to behave standard linear solid in shear and elastically in dilatation. Two-dimensional examples are solved under general temperature distributions T = T(x, t), and compared with other opproximate solutions to show the versatility of the presented analysis.

Improvement of dynamic encoding algorithm for searches (DEAS) using hopping unidirectional search (HUDS)

  • Choi, Seong-Chul;Kim, Nam-Gun;Kim, Jong-Wook;Kim, Sang-Woo
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2005년도 ICCAS
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    • pp.324-329
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    • 2005
  • Dynamic Encoding Algorithm for Searches (DEAS) which is known as a fast and reliable non-gradient optimization method, was proposed [1]. DEAS reaches local or global optimum with binary strings (or binary matrices for multi-dimensional problem) by iterating the two operations; bisectional search (BSS) and unidirectional search (UDS). BSS increases binary strings by one digit (i.e., 0 or 1), while UDS performs increment or decrement of binary strings in the BSS' result direction with no change of string length. Because the interval of UDS exponentially decreases with increment of bit string length (BSL), DEAS is difficult to escape from local optimum when DEAS falls into local optimum. Therefore, this paper proposes hopping UDS (HUDS) which performs UDS by hopping as many as BSL in the final point of UDS process. HUDS helps to escape from local optimum and enhances a probability searching global optimization. The excellent performance of HUDS will be validated through the well-known benchmark functions.

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Free Vibration Analysis of Monosymmetric Thin-walled Circular Curved Beam (일축대칭 단면을 갖는 박벽 원형 곡선보의 자유진동 해석)

  • 장승필;김문영;민병철
    • Journal of the Earthquake Engineering Society of Korea
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    • 제2권2호
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    • pp.57-68
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    • 1998
  • For free vibration of monosymmetric thin-walled circular arches including restrained warping effect, the elastic strain and kinetic energy is derived by introducing displacement fields of circular arches in which all displacement parameters are defined at the centroid axis. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. Analytical solution for free vibration behaviors of simply supported thin-walled curved beam element is presented by evaluating elastic stiffness and mass matrices. In order to illustrate the accuracy and practical usefulness of this study, analytical and numerical solutions for free vibration of circular arches are presented and compared with solutions analyzed by the FEM using straight beam element.

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MULTISPECTRAL IMAGING APPLICATION FOR FOOD INSPECTION

  • Park, Bosoon;Y.R.Chen
    • Proceedings of the Korean Society for Agricultural Machinery Conference
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    • 한국농업기계학회 1996년도 International Conference on Agricultural Machinery Engineering Proceedings
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    • pp.755-764
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    • 1996
  • A multispectral imaging system with selected wavelength optical filter was demonstrated feasible for food safety inspection. Intensified multispectral images of carcasses were obtained with visible/near-infrared optical filters(542-847 nm wavelengths) and analyzed. The analysis of textural features based on co-occurrence matrices was conducted to determine the feasibility of a multispectral image analyses for discriminating unwholesome poultry carcasses from wholesome carcasses. The mean angular second moment of the wholesome carcasses scanned at 542 nm wavelength was lower than that of septicemic (P$\leq$0.0005) and cadaver(P$\leq$0.0005) carcasses. On the other hand, for the carcasses scanned at 700nm wavelength , the feature values of septicemic and cadaver carcasses were significantly (P$\leq$0.0005) different from wholesome carcasses. The discriminant functions for classifying poultry carcasses into three classes (wholesome, septicemic , cadaver) were developed using linear and quadr tic covariance matrix analysis method. The accuracy of the quadratic discriminant models, expressed in rates of correct classification, were over 90% for the classification of wholesome, septicemic, and cadaver carcasses when textural features from the spectral images scanned at the wavelength of 542 and 700nm were utilized.

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