• Title/Summary/Keyword: integral type boundary value problem

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POSITIVE SOLUTIONS OF SELF-ADJOINT BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE

  • Yang, Aijun;Ge, Weigao
    • The Pure and Applied Mathematics
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    • v.15 no.4
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    • pp.407-414
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    • 2008
  • In this paper, we study the self-adjoint second order boundary value problem with integral boundary conditions: (p(t)x'(t))'+f(t,x(t))=0, t $${\in}$$ (0,1), x'(0)=0, x(1) = $${\int}_0^1$$ x(s)g(s)ds. A new result on the existence of positive solutions is obtained. The interesting points are: the first, we employ a new tool-the recent Leggett-Williams norm-type theorem for coincidences; the second, the boundary value problem is involved in integral condition; the third, the solutions obtained are positive.

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A boundary radial point interpolation method (BRPIM) for 2-D structural analyses

  • Gu, Y.T.;Liu, G.R.
    • Structural Engineering and Mechanics
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    • v.15 no.5
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    • pp.535-550
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    • 2003
  • In this paper, a boundary-type meshfree method, the boundary radial point interpolation method (BRPIM), is presented for solving boundary value problems of two-dimensional solid mechanics. In the BRPIM, the boundary of a problem domain is represented by a set of properly scattered nodes. A technique is proposed to construct shape functions using radial functions as basis functions. The shape functions so formulated are proven to possess both delta function property and partitions of unity property. Boundary conditions can be easily implemented as in the conventional Boundary Element Method (BEM). The Boundary Integral Equation (BIE) for 2-D elastostatics is discretized using the radial basis point interpolation. Some important parameters on the performance of the BRPIM are investigated thoroughly. Validity and efficiency of the present BRPIM are demonstrated through a number of numerical examples.

Existence and Non-Existence of Positive Solutions of BVPs for Singular ODEs on Whole Lines

  • LIU, YUJI;YANG, PINGHUA
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.997-1030
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    • 2015
  • This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

On Computation of the Stress Intensity Factors in the V-Notched Plates using a contour integral method (경로적분법 을 이용한 V-노치 평판 의 응력확대계수 계산)

  • 김진우;김선덕;홍창선
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.8 no.3
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    • pp.232-240
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    • 1984
  • The plane elastostatic boundary value problem with the sharp V-notched singularity is formulated by a contour integral method for determining numerically the stress intensity factors. The integral formula is based on Somigliana type of reciprocal work in terms of displacement and traction vectors on the plate boundary. The characteristic singular solutions can be identified on the basis of traction free boundary conditions of two radial notch edges. Two numerical example examples are treated in detail; a symmetric mode-I type of notched plate with various interior angles and a mixed mode type of cantilever subjected to end shear.

On the Vorticity and Pressure Boundary Conditions for Viscous Incompressible Flows (비압축성 점성유동의 와도와 압력 경계조건)

  • Suh J.-C.
    • 한국전산유체공학회:학술대회논문집
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    • 1998.05a
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    • pp.15-28
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    • 1998
  • As an alternative for solving the incompressible Navier-Stokes equations, we present a vorticity-based integro-differential formulation for vorticity, velocity and pressure variables. One of the most difficult problems encountered in the vorticity-based methods is the introduction of the proper value-value of vorticity or vorticity flux at the solid surface. A practical computational technique toward solving this problem is presented in connection with the coupling between the vorticity and the pressure boundary conditions. Numerical schemes based on an iterative procedure are employed to solve the governing equations with the boundary conditions for the three variables. A finite volume method is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition . The velocity field is obtained by using the Biot-Savart integral derived from the mathematical vector identity. Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well-established for potential flow analysis. The calculated results with the present mettled for two test problems are compared with data from the literature in order for its validation. The first test problem is one for the two-dimensional square cavity flow driven by shear on the top lid. Two cases are considered here: (i) one driven both by the specified non-uniform shear on the top lid and by the specified body forces acting through the cavity region, for which we find the exact solution, and (ii) one of the classical type (i.e., driven only by uniform shear). Secondly, the present mettled is applied to deal with the early development of the flow around an impulsively started circular cylinder.

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Mechanical Behavior of Fiber Metal Laminates with Local Delamination Defects (국부적 적층분리결함을 갖는 섬유금속적층판의 기계적 거동 특성)

  • Choi, Heungsoap;Choi, Hyungjip;Choi, Wonjong;Ha, Minsu
    • Journal of Aerospace System Engineering
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    • v.1 no.1
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    • pp.25-35
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    • 2007
  • In this paper, the interlaminar crack problems of a fiber metal laminate (FML) under generalized plane deformation are studied using the theory of anisotropic elasticity. The crack is considered to be embedded in the matrix interlaminar region (including adhesive zone and resin rich zone) of the FML. Based on Fourier integral transformation and the stress matrix formulation, the current mixed boundary value problem is reduced to solving a system of Cauchy-type singular integral equations of the 1st kind. Within the theory of linear fracture mechanics, the stress intensity factors are defined on terms of the solutions of integral equations and numerical results are obtained for in-plane normal (mode I) crack surface loading. The effects of location and length of crack in the 3/2 and 2/1 ARALL, GLARE or CARE type FML's on the stress intensity factors are illustrated.

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BLOW UP OF SOLUTIONS FOR A PETROVSKY TYPE EQUATION WITH LOGARITHMIC NONLINEARITY

  • Jorge, Ferreira;Nazli, Irkil;Erhan, Piskin;Carlos, Raposo;Mohammad, Shahrouzi
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.6
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    • pp.1495-1510
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    • 2022
  • This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.

Optimal Solution of a Cyclic Task Using the Global Path Information for a Redundant Robot (여유자유도 로봇에 있어서 광역의 경로정보를 이용한 주기작업의 최적해)

  • 최병욱;원종화;정명진
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.29B no.3
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    • pp.6-15
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    • 1992
  • This paper proposes a method for the global optimization of redundancy over the whole task period for a kinematically redundant robot. The necessary conditions based on the calculus of variations for an integral type cost criterion result in a second-order differential equation. For a cyclic task, the periodic boundary conditions due to conservativity requirements are discussed. We refine the two-point boundary value problem to an initial value adjustment problem and suggest a numerical search method for providing the conservative global optimal solution using the gradient projection method. Since the initial joint velocity is parameterized with the number of the redundancy, we only search the parameter value in the space of as many dimensions as the number of degrees of redundancy. We show through numerical examples that multiple nonhomotopic extremal solutions and the generality of the proposed method by considering the dynamics of a robot.

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A 3-Dimentional Radiation Diffraction Problem Analysis by B-Spline Higher-Order Panel Method

  • Kim Gun-Do;Lee Chang-Sup
    • Journal of Ship and Ocean Technology
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    • v.10 no.1
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    • pp.10-26
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    • 2006
  • The radiation problem for oscillating bodies on the free surface has been formulated by the over-determined Green integral equation, where the boundary condition on the free surface is satisfied by adopting the Kelvin-type Green function and the irregular frequencies are removed by placing additional control points on the free surface surrounded by the body. The B-Spline based higher order panel method is then applied to solve the problem numerically. Because both the body geometry and the potential on the body surface are represented by the B-Splines, that is in polynomials of space parameters, the unknown potential can be determined accurately to the order desired above the constant value. In addition, the potential expressed in B-Spline can be differentiated analytically to get the velocity on the surface without introducing any numerical error. Sample computations are performed for a semispherical body and a rectangular box floating on the free surface for six-degrees of freedom motions. The added mass and damping coefficients are compared with those by the already-validated constant panel method of the same formulation showing strikingly good agreements.

A Numerical Analysis on the solution of Poisson Equation by Direct Method (직접법을 이용한 Poisson 방정식 수치해법에 관하여)

  • Y.S. Shin;K.P. Rhee
    • Journal of the Society of Naval Architects of Korea
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    • v.32 no.3
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    • pp.62-71
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    • 1995
  • In the numerical analysis of incompressible unsteady Navier-stokes equation, large time is required for solving the pressure Poisson equation of the elliptic type at each time step. In this paper, a numerical analysis by the direct method is carried out to solve the pressure Poisson equation and the computing time is analyzed as mesh size increases. The pressure Poisson equation can be transformed to the boundary value problem by the Green theorem. The computing time for the convolution type of the domain integral can be reduced by using F.F.T. and the computing time in the direct method depends entirely on obtaining the solution of the boundary value problem. The numerical analysis on the known solutions is carried out and compared for the verification of the direct method. And the numerical analysis on the body boundary and domain decomposition problem are carried out with the computing time less than O($n^{3}$) in the (n.n) mesh.

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