Computations of Arbitrary Thin-Shell Vertical Cylinders in a Wave Field by a Hypersingular Integral-Equation Method

2014 ◽  
Author(s):  
Mohamed Hariri Nokob ◽  
Ronald W. Yeung
Keyword(s):  
Integral Equation ◽  
Thin Shell ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Hypersingular Integral Equation ◽  
Wave Load ◽  
Hypersingular Integral ◽  
Method Of Solution ◽  
Vertical Cylinders

We present a numerical formulation and computational results for the hydrodynamic loads on bottom-mounted thin-shell vertical cylinders of arbitrary cross-sectional shapes, including open bodies. Such cylinders may undergo prescribed or free motion or may be subjected to a wave load. The formulation is based on linear theory and a hypersingular integral-equation results from sectional contours of zero thickness. The method reduces the fully three-dimensional problem into a number of two-dimensional ones in the horizontal plane and is therefore much faster than the usual boundary integral method used for water wave problems. This traditional method of solution is also known to become ill-conditioned as the body thickness decreases. As an example of the current method, radiation and diffraction loads are presented for the cases of a circular and square closed and opened cylinders with the effect of the increased opening size discussed at different frequencies. The free-surface elevation associated with this method of solution is presented for some cases as well.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

Analysis of Crack Propagation in Roller Bearings Using the Boundary Integral Equation Method—A Mixed-Mode Loading Problem

1988 ◽  
Vol 110 (3) ◽  
pp. 408-413 ◽  
Author(s):  
L. J. Ghosn
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Crack Propagation ◽  
Boundary Integral Equation ◽  
Stress Intensity Factors ◽  
High Speed ◽  
Roller Bearing ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Intensity Factors

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

scholarly journals Computation of Energy Release Rates for a Nearly Circular Crack

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Nik Mohd Asri Nik Long ◽  
Lee Feng Koo ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Integral Equation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Linear Equations ◽  
Circular Crack ◽  
Plane Elasticity ◽  
Hypersingular Integral Equation ◽  
Hypersingular Integral ◽  
Energy Release Rates

This paper deals with a nearly circular crack, in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, and it is then transformed into a similar equation over a circular region, , using conformal mapping. Appropriate collocation points are chosen on the region to reduce the hypersingular integral equation into a system of linear equations with unknown coefficients, which will later be used in the determination of energy release rate. Numerical results for energy release rate are compared with the existing asymptotic solution and are displayed graphically.

The boundary integral equation for curved solid/liquid interfaces propagating into a binary liquid with convection

2021 ◽  
Author(s):  
Ekaterina Titova ◽  
Dmitri Alexandrov
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Curvilinear Coordinates ◽  
Forced Flow ◽  
Function Technique ◽  
Liquid Interfaces ◽  
Convective Boundary ◽  
Solid Liquid

Abstract The boundary integral method is developed for unsteady solid/liquid interfaces propagating into undercooled binary liquids with convection. A single integrodifferential equation for the interface function is derived using the Green function technique. In the limiting cases, the obtained unsteady convective boundary integral equation (CBIE) transforms into a previously developed theory. This integral is simplified for the steady-state growth in arbitrary curvilinear coordinates when the solid/liquid interface is isothermal (isoconcentration). Finally, we evaluate the boundary integral for a binary melt with a forced flow and analyze how the melt undercooling depends on P\'eclet and Reynolds numbers.

scholarly journals An integral equation–based numerical method for the forced heat equation on complex domains

2020 ◽  
Vol 46 (5) ◽  
Author(s):  
Fredrik Fryklund ◽  
Mary Catherine A. Kropinski ◽  
Anna-Karin Tornberg
Keyword(s):  
Integral Equation ◽  
Heat Equation ◽  
Helmholtz Equation ◽  
Singular Integrals ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Elliptic Pdes ◽  
Time Step ◽  
Modified Helmholtz Equation ◽  
High Regularity

Abstract Integral equation–based numerical methods are directly applicable to homogeneous elliptic PDEs and offer the ability to solve these with high accuracy and speed on complex domains. In this paper, such a method is extended to the heat equation with inhomogeneous source terms. First, the heat equation is discretised in time, then in each time step we solve a sequence of so-called modified Helmholtz equations with a parameter depending on the time step size. The modified Helmholtz equation is then split into two: a homogeneous part solved with a boundary integral method and a particular part, where the solution is obtained by evaluating a volume potential over the inhomogeneous source term over a simple domain. In this work, we introduce two components which are critical for the success of this approach: a method to efficiently compute a high-regularity extension of a function outside the domain where it is defined, and a special quadrature method to accurately evaluate singular and nearly singular integrals in the integral formulation of the modified Helmholtz equation for all time step sizes.

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