scholarly journals Ultra-weak Formulation of a Hypersingular Integral Equation on Polygons and DPG Method with Optimal Test Functions

2014 ◽  
Vol 52 (6) ◽  
pp. 2703-2721 ◽  
Author(s):  
Norbert Heuer ◽  
Felipe Pinochet
Keyword(s):  
Integral Equation ◽  
Hypersingular Integral Equation ◽  
Test Functions ◽  
Optimal Test ◽  
Weak Formulation ◽  
Hypersingular Integral

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.

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.

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