Integral equation solutions for simply supported polygonal plates

Maiti, Manoranjan; Chakrabarty, S. K.

doi:10.1016/0020-7225(74)90017-2

Cited by 48 publications

(7 citation statements)

References 6 publications

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“…As in the biharmonic MFS considered in [12], which is based on the simple layer potential representation of [11,17], we approximate the solution u of (2. …”

Section: Mfs Formulationmentioning

confidence: 99%

A matrix decomposition MFS algorithm for axisymmetric biharmonic problems

2005

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We consider the approximate solution of axisymmetric biharmonic problems using a boundary-type meshless method, the Method of Fundamental Solutions (MFS) with fixed singularities and boundary collocation. For such problems, the coefficient matrix of the linear system defining the approximate solution has a block circulant structure. This structure is exploited to formulate a matrix decomposition method employing fast Fourier transforms for the efficient solution of the system. The results of several numerical examples are presented.

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“…As in the biharmonic MFS considered in [12], which is based on the simple layer potential representation of [11,17], we approximate the solution u of (2. …”

Section: Mfs Formulationmentioning

confidence: 99%

A matrix decomposition MFS algorithm for axisymmetric biharmonic problems

2005

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“…Here the (t, n) axes form a right-handed set so that, in an obvious notation, V~,n)f = VL,y)f (15) for any sufficiently differentiable function f.…”

Section: Governing Equationsmentioning

confidence: 99%

“…The All of the integrals in the discretised equations were evaluated analytically to maintain accuracy at the present stage: the integrals associated with the G 2 and G2, functions have previously been obtained numerically [15]. Details of the analytic integrations are given by Kelmanson [16].…”

Section: Numerical Solutionmentioning

confidence: 99%

Boundary integral equation solution of viscous flows with free surfaces

Kelmanson

1983

J Eng Math

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Solutions of the biharmonic equation governing steady two-dimensional viscous flow of an incompressible Newtonian fluid are obtained by employing a direct biharmonic boundary integral equation (BBIE) method in which Green's theorem is used to reformulate the differential equation as a pair of coupled integral equations which are applied only on the boundary of the solution domain.An iterative modification of the classical BBIE is presented which is able to solve a large class of (nonlinear) viscous free surface flows for a wide range of surface tensions. The method requires a knowledge of the asymptotic behaviour of the free surface profile in the limiting case of infinite surface tension but this can usually be obtained from a perturbation analysis. Unlike space discretisation techniques such as finite difference or finite element, the BBIE evaluates only boundary information on each iteration. Once the solution is evaluated on the boundary the solution at interior points can easily be obtained.

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“…Later indirect boundary integral equation for Kirchhoff plate bending problems was presented by Altiero and Sikarskie (1978) and Tottenham (1979). Direct boundary integral formulations can be found in Maiti and Chakrabarty (1974), Stern (1981) and Hartmann and Zotemantel (1986). For the Reissner/Mindlin plate model (Reissner, 1947), the boundary integral equation was reported by Vander Weeën (1982) for static problems, who used the Hormander method to derive the fundamental solutions.…”

Section: Introductionmentioning

confidence: 98%

Displacement Discontinuity Method for Fracture Mechanics Analysis of Reissner Plates: Static and Dynamic

2005

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International Journal of Fracture (2005) 135:95-116 Abstract. This paper is concerned with the displacement discontinuity method applied to the shear deformable plates (Reissner's and Mindlin's theories) with cracks subjected to static and dynamic loads. Fundamental solutions of dislocation are derived using the Fourier transform method and the Laplace transformation technique. Boundary integral equations are presented in terms of rotations/displacement on the crack surfaces. The Chebyshev polynomials of the second kind are used to evaluate the integral equations with hypersingular kernels on the crack boundaries and determine the stress intensity factors at the crack tips. Comparisons are made with other numerical solutions to demonstrate the proposed method is accurate both for static and dynamic problems.

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Integral equation solutions for simply supported polygonal plates

Cited by 48 publications

References 6 publications

A matrix decomposition MFS algorithm for axisymmetric biharmonic problems

A matrix decomposition MFS algorithm for axisymmetric biharmonic problems

Boundary integral equation solution of viscous flows with free surfaces

Displacement Discontinuity Method for Fracture Mechanics Analysis of Reissner Plates: Static and Dynamic

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