• Title/Summary/Keyword: Higher order polynomial

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The buckling of rectangular plates with opening using a polynomial method

  • Muhammad, T.;Singh, A.V.
    • Structural Engineering and Mechanics
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    • v.21 no.2
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    • pp.151-168
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    • 2005
  • In this paper an energy method is presented for the linear buckling analysis of first order shear deformable plates. The displacement fields are defined in terms of the shape functions, which correspond to a set of predefined points and are composed of significantly high order polynomials. The locations of these points are found by mapping the geometry using the naturalized coordinates and bilinear shape functions. In order to evaluate the method, fully clamped and simply supported rectangular plates subjected to uniform uniaxial compressive loading on two opposite edges of the plate are investigated thoroughly and the results are compared with the exact solution given in the monograph of Timoshenko and Gere (1961). The method is extended to the analysis of perforated plates, wherein the negative stiffness computed over the opening area from in-plane and out-of-plane deformation modes is superimposed to the stiffness of the full plate. Numerical results are then favorably compared with those obtained by finite element methods. Other cases such as; rectangular plates with eccentrically located openings of different shapes are studied and reported in this paper with regards to the effect of aspect ratio, hole size, and hole position on the buckling. For a square plate with a large circular opening at the center, diameter being 80 percent of the length, the present method yields buckling coefficient 12.5 percent higher than the one from the FEM.

Free vibration analysis of arbitrary shape plates with simplified series function (단순급수함수를 이용한 임의 형상판의 자유진동 해석)

  • 정대근
    • Journal of KSNVE
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    • v.5 no.3
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    • pp.345-352
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    • 1995
  • A very simple and computationally efficient numerical method is developed for the free vibration of arbitrary shape plates. A set of two- dimensional simple series functions is used as an admissible displacement functions in the Rayleigh-Ritz method to obtain the natural frequencies for the arbitrary shape plates. From the prescribed starting function satisfying only the geometric boundary conditions, the higher terms in the series function are constructed with adding order of polynomial. Natural frequencies are obtained for the arbitrary shape plates, with combinational boundary conditions. The obtained numerical results are presented, some cases are verified with other numerical methods in the literature.

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Translation method: a historical review and its application to simulation of non-Gaussian stationary processes

  • Choi, Hang;Kanda, Jun
    • Wind and Structures
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    • v.6 no.5
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    • pp.357-386
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    • 2003
  • A number of methods based on various ideas have been proposed for simulating the non-Gaussian stationary process. However, these methods have some limitations. This paper reviewed several simulation methods based on the translation method using logarithmic and polynomial functions, which have emerged in the history of statistics and in the field of civil engineering. The applicability of each method is discussed from the viewpoint of the reproducibility of higher order statistics of the object function in the simulated sample functions, and examined using pressure signals measured from wind tunnel experiments for various shapes of buildings. The parameter estimation methods, i.e. the method of moments and quantile plot, are also reviewed, and the useful aspects of each method are discussed. Additionally, a simple worksheet for parameter estimation is derived based on the method of moment for practical application, and the accuracy is discussed comparing with a set of previously proposed formulae.

Implementation of Fuzzy Self-Organizing Networks Algorithm and Its Application to Nonlinear Systems (퍼지 자기구성 네트워크 알고리즘의 구현 및 비선형 시스템으로의 응용)

  • Park, Byoung-Jun;Kim, Dong-Won;Lee, Dae-Keun;Oh, Sung-Kwun
    • Proceedings of the KIEE Conference
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    • 2000.07d
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    • pp.3001-3003
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    • 2000
  • In this paper. we propose Fuzzy Self-Organizing Networks (FSON) using both Polynomial Neural Networks(PNN) and Fuzzy Neural Networks(FNN) for model identification of complex and nonlinear systems. The proposed FSON is generated from the mutually combined structure of both FNN and PNN. Accordingly it is possible to consider the nonlinearity characteristics of process and to get the better output performance with superb predictive ability. In order to evaluate the performance of proposed models. we use the nonlinear data sets. The results show that the proposed FSON can produce the model with higher accuracy and more robustness than previous any other method.

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An Image Coding Technique Using the Image Segmentation (영상 영역화를 이용한 영상 부호화 기법)

  • 정철호;이상욱;박래홍
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.24 no.5
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    • pp.914-922
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    • 1987
  • An image coding technique based on a segmentation, which utilizes a simplified description of regions composing an image, is investigated in this paper. The proposed coding technique consists of 3 stages: segmentation, contour coding. In this paper, emphasis was given to texture coding in order to improve a quality of an image. Split-and-merge method was employed for a segmentation. In the texture coding, a linear predictive coding(LPC), along with approximation technique based on a two-dimensional polynomial function was used to encode texture components. Depending on a size of region and a mean square error between an original and a reconstructed image, appropriate texture coding techniques were determined. A computer simulation on natural images indicates that an acceptable image quality at a compression ratio as high as 15-25 could be obtained. In comparison with a discrete cosine transform coding technique, which is the most typical coding technique in the first-generation coding, the proposed scheme leads to a better quality at compression ratio higher than 15-20.

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Krawtchouk Polynomial Approximation for Binomial Convolutions

  • Ha, Hyung-Tae
    • Kyungpook Mathematical Journal
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    • v.57 no.3
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    • pp.493-502
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    • 2017
  • We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

A Compilation and Evaluation of Thermal and Mechanical Properties of Bentonite-based Buffer Materials for a High- level Waste Repository

  • Cho, Won-Jin;Lee, Jae-Owan;Kang, Chul-Hyung
    • Nuclear Engineering and Technology
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    • v.34 no.1
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    • pp.90-103
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    • 2002
  • The thermal and mechanical properties of compacted bentonite and bentonite-sand mixture were collected from the literatures and compiled. The thermal conductivity of bentonite is found to increase almost linearly with increasing dry density and water content of the bentonite. The specific heat can also be expressed as a function of water ontent, and the coefficient of thermal expansion is almost independent on the dry density. The logarithm of unconfined compressive strength and Young’s modulus of elasticity increase linearly with increasing dry density, and in the case of constant dry density, it can be fitted to a second order polynomial of water content. Also the unconfined compressive strength and Young’s modulus of elasticity of the bentonite-sand mixture decreases with increasing sand content. The Poisson’s ratio remains constant at the dry density higher than 1.6 Mg/m$_3$, and the shear strength increases with increasing dry density.

Numerical frequency analysis of skew sandwich layered composite shell structures under thermal environment including shear deformation effects

  • Katariya, Pankaj V.;Panda, Subrata K.
    • Structural Engineering and Mechanics
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    • v.71 no.6
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    • pp.657-668
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    • 2019
  • The numerical thermal frequency responses of the skew sandwich shell panels structure are investigated via a higher-order polynomial shear deformation theory including the thickness stretching effect. A customized MATLAB code is developed using the current mathematical model for the computational purpose. The finite element solution accuracy and consistency have been checked via solving different kinds of numerical benchmark examples taken from the literature. After confirming the standardization of the model, it is further extended to show the effect of different important geometrical parameters such as span-to-thickness ratios, aspect ratios, curvature ratios, core-to-face thickness ratios, skew angles, and support conditions on the frequencies of the sandwich composite flat/curved panel structure under elevated temperature environment.

Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel

  • Dash, Sushmita;Mehar, Kulmani;Sharma, Nitin;Mahapatra, Trupti Ranjan;Panda, Subrata Kumar
    • Earthquakes and Structures
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    • v.16 no.1
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    • pp.55-67
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    • 2019
  • The finite solutions of deflection and the corresponding in-plane stress values of the graded sandwich shallow shell structure are computed in this research article via a higher-order polynomial shear deformation kinematics. The shell structural equilibrium equation is derived using the variational principle in association with a nine noded isoprametric element (nine degrees of freedom per node). The deflection values are computed via an own customized MATLAB code including the current formulation. The stability of the current finite element solutions including their accuracies have been demonstrated by solving different kind of numerical examples. Additionally, a few numerical experimentations have been conducted to show the influence of different design input parameters (geometrical and material) on the flexural strength of the graded sandwich shell panel including the geometrical configurations.

Application of the Visioplasticity Method to the Axisymmetric Bulk Deformation Processes (축대칭소성가공에 있어서의 변형가시화법의 응용에 대한 연구)

  • Bai, Duck-Han
    • Journal of the Korean Society for Precision Engineering
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    • v.2 no.2
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    • pp.31-42
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    • 1985
  • The metal flow and the strain distribution is investigated for the steady state and non-steady state bulk deformation processes by using an improved visioplasticity method which includes the effective smoothing scheme. The comparison of various smoothing schemes leads to the selection of the five- point least square smoothing method which is employed to reduce the measurement errors. As a steady state forming process experiments are carried out for axisy- mmetric forward extrusion through conical and curved dies of various area reduc- tions using Aluminum and steel billets. Axisymmetric backward extrusion is chosen for a nonsteady state forming process. In axisymmetric forward extrusion the results from visioplasticity show that the curved die of a fourth-order polynomial renders more uniform distribution of strain rates and strains. Higher reduction leads to greater strain rates at the outer side of the billet. The visioplastic observation for axisymmetric backward extrusion as a non-steady state deformation process shows the concentration of higher strain at the inner wall of the extruded product. The visioplastic results in forward extrusion are in agreement with the computed results by the finite element method. It is thus shown that the visio- plasticity combined with a smoothing technique is an effective method to determine the pattern and the distribution of strain rates and strains.

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