• Title/Summary/Keyword: Kirchhoff Method

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ON SOME p(x)-KIRCHHOFF TYPE EQUATIONS WITH WEIGHTS

  • Chung, Nguyen Thanh
    • Journal of applied mathematics & informatics
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    • v.32 no.1_2
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    • pp.113-128
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    • 2014
  • Consider a class of p(x)-Kirchhoff type equations of the form $$\left\{-M\left({\int}_{\Omega}\;\frac{1}{p(x)}{\mid}{\nabla}u{\mid}^{p(x)}\;dx\right)\;div\;({\mid}{\nabla}u{\mid}^{p(x)-2}{\nabla}u)={\lambda}V(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u=0\;on\;{\partial}{\Omega},$$ where p(x), $q(x){\in}C({\bar{\Omega}})$ with 1 < $p^-\;:=inf_{\Omega}\;p(x){\leq}p^+\;:=sup_{\Omega}p(x)$ < N, $M:{\mathbb{R}}^+{\rightarrow}{\mathbb{R}}^+$ is a continuous function that may be degenerate at zero, ${\lambda}$ is a positive parameter. Using variational method, we obtain some existence and multiplicity results for such problem in two cases when the weight function V (x) may change sign or not.

Truncated hierarchical B-splines in isogeometric analysis of thin shell structures

  • Atri, H.R.;Shojaee, S.
    • Steel and Composite Structures
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    • v.26 no.2
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    • pp.171-182
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    • 2018
  • This paper presents an isogeometric discretization of Kirchhoff-Love thin shells using truncated hierarchical B-splines (THB-splines). It is demonstrated that the underlying basis functions are ideally appropriate for adaptive refinement of the so-called thin shell structures in the framework of isogeometric analysis. The proposed approach provides sufficient flexibility for refining basis functions independent of their order. The main advantage of local THB-spline evaluation is that it provides higher degree analysis on tight meshes of arbitrary geometry which makes it well suited for discretizing the Kirchhoff-Love shell formulation. Numerical results show the versatility and high accuracy of the present method. This study is a part of the efforts by the authors to bridge the gap between CAD and CAE.

A Comparative Study on the Displacement Behaviour of Triangular Plate Elements (삼각형 판 요소의 변위 거동에 대한 비교 연구)

  • 이병채;이용주;구본웅
    • Computational Structural Engineering
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    • v.5 no.2
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    • pp.105-118
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    • 1992
  • Static performance was compared for the triangular plate elements through some numerical experiments. Four Kirchhoff elements and six Mindlin elements were selected for the comparison. Numerical tests were executed for the problems of rectangular plates with regular and distorted meshes, rhombic plates, circular plates and cantilever plates. Among the Kirchhoff 9 DOF elements, the discrete Kirchhoff theory element was the best. Element distortion and the aspect ratio were shown to have negligible effects on the displacement behaviour. The Specht's element resulted in better results than the Bergan's but it was sensitive to the aspect ratio. The element based on the hybrid stress method also resulted in good results but it assumed to be less reliable. Among the linear Mindlin elements, the discrete shear triangle was the best in view of reliability, accuracy and convergence. Since the thin plate behaviour of it was as good as the DKT element, it can be used effectively in the finite element code regardless of the thickness. As a quadratic Mindlin element, the MITC7 element resulted in best results in almost all cases considered. The results were at least as good as those of doubly refined meshes of linear elements.

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Existence, Blow-up and Exponential Decay Estimates for the Nonlinear Kirchhoff-Carrier Wave Equation in an Annular with Robin-Dirichlet Conditions

  • Ngoc, Le Thi Phuong;Son, Le Huu Ky;Long, Nguyen Than
    • Kyungpook Mathematical Journal
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    • v.61 no.4
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    • pp.859-888
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    • 2021
  • This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annulus associated with Robin-Dirichlet conditions. At first, by applying the Faedo-Galerkin method, we prove existence and uniqueness results. Then, by constructing a Lyapunov functional, we prove a blow up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak solutions.

Sheet Forming Anlysis by Using Hierarchical Contact Searching Method (계층적 접촉 탐색방법을 이용한 박판성형 공정해석)

  • 김일권;김용한
    • Transactions of Materials Processing
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    • v.9 no.3
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    • pp.274-283
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    • 2000
  • A dynamic explicit finite element code for simulating sheet forming processes has been developed. The code utilizes the discrete Kirchhoff shell element and contact force is treated by a conventional penalty method. In order to reduce the computational cost, a new and robust contact searching algorithm has been developed and implemented into the code. In the method, a hierarchical structure of tool segments is built for each tool at the initial stage of the analysis. hierarchical structure is built in a way to divide a box to 8 sub-boxes, 2 in each direction, until the lowest level of the hierarchical structure contains exactly one segment of the tool or empty. Then at each time step, contact is checked from the box to sub-boxes hierarchically for each node. Comparisons of computational results of various examples with the existing ones show the validity of the method.

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BLADE PLANFORM OPTIMIZATION FOR HSI NOISE REDUCTION OF HELICOPTER (헬리콥터의 고속충격소음 감소를 위한 블레이드 평면형상 최적화)

  • Chae, Sang-Hyun;Yang, Choong-Mo;Jung, Shin-Kyu;Aoyama, Takashi;Obayashi, Shigeru;Yee, Kwang-Jung
    • Journal of computational fluids engineering
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    • v.14 no.1
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    • pp.53-61
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    • 2009
  • The objective of this research is to design blade planform to reduce high speed impulsive(HSI) noise from a non-lifting helicopter rotor using CFD method and optimization techniques. As for the aero-acoustic analysis, CFD technique for aerodynamic analysis and Kirchhoff's method for the acoustic analysis were used. As for the optimization method, Kriging-based genetic algorithm(GA) model as a high-fidelity optimization method was chosen. Design variables and constraints are determined for arbitrary blade planform. The result shows that the optimized blade planform with high swept-back and taper ratio can reduce HSI noise by suppressing generation of the strong shock wave on blade surface and propagation of the noise to the farfield flow region.

An Analysis of the Flow and Sound Field of a Ducted Axial Fan (덕트가 있는 축류홴의 유동 및 음향장 해석)

  • Jeon, Wan Ho;Chung, Ki Hoon;Lee, Duck Joo
    • 유체기계공업학회:학술대회논문집
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    • 1999.12a
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    • pp.208-217
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    • 1999
  • The present work describes the prediction method for the unsteady flow field and the acoustic pressure field of a ducted axial fan. The prediction method is comprised of time-marching free-wake method, acoustic analogy, and the Helmholtz-Kirchhoff BEM. The predicted sound signal of a rotor is similar to the experiment one. We assume that the rotor rotates with a constant angular velocity and the flow field around the rotor is incompressible and inviscid. Then, a time-marching free-wake method is used to model the fan and to calculate the flow field. The force of each element on the blade is calculated by the unsteady Bernoulli equation. Lowson's method is used to predict the acoustic source. The newly developed Helmholtz-Kirchhoff BEM for thin body is used to calculate the sound field of the ducted fan. The ducted fan with 6 blades is analysed and the sound field around the duct is calculated.

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Determining the target strength bambood wrasse (Pseudolabrus japonicus) using Kirchhoff-ray mode

  • Kusdinar, Afriana;Hwang, Bo-Kyu;Shin, Hyeon-Ok
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.50 no.4
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    • pp.427-434
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    • 2014
  • Although ex situ target strength (TS) measurements using dual- and split-beam systems have become the primary approach of estimating fish abundance, theoretical model estimation is a powerful tool for verifying the measurements, as well as for providing values when making direct measurements is difficult. TS values for 20 samples of live bambooleaf wrasse (Pseudolabrus japonicus) whose target length (TL) ranged between 13.7 and 21.3 cm were estimated theoretically using the Kirchhoff-ray mode model, and the TS values for 18 live fish samples were additionally measured at ${\sim}0^{\circ}$ tilt angle to the swimming aspect using a tethered method at a frequency of 120 kHz to verify the theoretical values. The digitizing intervals used to extract the fish body and swim bladder morphology in the X-ray photographs significantly affected the calculated TS patterns, but variations based on the speed of sound and density ratio values for the general range of fish flesh were relatively small (within 1 dB). Close agreement was observed between the measured and theoretical TS values, and the correlation between the average TS and body length of the fish could be calculated accurately as <$TS_{120kHz}$>= 20logTL (cm) -71.6 using the theoretical method.

Buckling of rectangular plates with mixed edge supports

  • Xiang, Y.;Su, G.H.
    • Structural Engineering and Mechanics
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    • v.14 no.4
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    • pp.401-416
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    • 2002
  • This paper presents a domain decomposition method for buckling analysis of rectangular Kirchhoff plates subjected to uniaxial inplane load and with mixed edge support conditions. A plate is decomposed into two rectangular subdomains along the change of the discontinuous support conditions. The automated Ritz method is employed to derive the governing eigenvalue equation for the plate system. Compatibility conditions are imposed for transverse displacement and slope along the interface of the two subdomains by modifying the Ritz trial functions. The resulting Ritz function ensures that the transverse displacement and slope are continuous along the entire interface of the two subdomains. The validity and accuracy of the proposed method are verified with convergence and comparison studies. Buckling results are presented for several selected rectangular plates with various combination of mixed edge support conditions.

A Study on the Detection of Small Cavity Located in the Hard Rock by Crosswell Seismic Survey (경암 내 소규모 공동 탐지를 위한 시추공간 탄성파탐사 기법의 적용성 연구)

  • Ko, Kwang-Beom;Lee, Doo-Sung
    • Geophysics and Geophysical Exploration
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    • v.6 no.2
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    • pp.57-63
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    • 2003
  • For the dectection of small cavity in the hard rock, we investigated the feasibility of crosswell travel-time tomography and Kirchhoff migration technique. In travel-time tomography, first arrival anomaly caused by small cavity was investigated by numerical modeling based on the knowledge of actual field information. First arrival delay was very small (<0.125 msec) and detectable receiver offset range was limited to 4m with respect to $1\%$ normalized first arrival anomaly. As a consequence, it was turned out that carefully designed survey array with both sufficient narrow spatial spacing and temporal (<0.03125 msec) sampling were required for small cavity detection. Also, crosswell Kirchhoff migration technique was investigated with both numerical and real data. Stack section obtained by numerical data shows the good cavity image. In crosswell seismic data, various unwanted seismic events such as direct wave and various mode converted waves were alto recorded. To remove these noises und to enhance the diffraction signal, combination of median and bandpass filtering was applied and prestack and stacked migration images were created. From this, we viewed the crosswell migration technique as one of the adoptable method for small cavity detection.