Analysis of Elastic Torsion in a Bar With Circular Holes by a Special Boundary Integral Method

1983 ◽  
Vol 50 (1) ◽  
pp. 101-108 ◽  
Author(s):  
D. A. Caulk
Keyword(s):  
Integral Equations ◽  
Cross Section ◽  
Boundary Integral Equations ◽  
Torsional Rigidity ◽  
Circular Cross Section ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Warping Function ◽  
Special Boundary ◽  
Circular Holes

Special boundary integral equations developed in an earlier paper are generalized here for torsion of an elastic bar with circular holes. In this approach, the solution on the boundary of each hole is represented by a series of circular harmonics, and the coefficients in these series are determined by a special system of boundary integral equations. For a cross section with only one hole, the entire system of equations is reduced without approximation to a single integral equation involving only the warping function on the outer boundary. For multiple holes, approximate equations are derived that retain only the first harmonic in the solution representation on each hole. The latter equations are solved analytically for a circular cross section weakened by a concentric ring of circular holes. Simple expressions are derived for torsional rigidity, warping, and maximum stress. The results for torsional rigidity are an improvement over previous ones obtained by another approximate method.

Special Boundary Integral Equations for Potential Problems in Regions With Circular Holes

1984 ◽  
Vol 51 (4) ◽  
pp. 713-716 ◽  
Author(s):  
D. A. Caulk
Keyword(s):  
Integral Equations ◽  
Infinite System ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Special Boundary ◽  
Laplace's Equation ◽  
Special Cases ◽  
Potential Problems ◽  
Circular Holes

An infinite system of special boundary integral equations is derived for the solution of Laplace’s equation in a general two-dimensional region with circular holes. The solution is shown to converge when the number of holes is finite and no two holes are touching. In special cases, these equations are shown to yield the same results as two more restricted methods, which are based on different approaches.

Flow of a spherical capsule in a pore with circular or square cross-section

2011 ◽  
Vol 705 ◽  
pp. 176-194 ◽  
Author(s):  
X.-Q. Hu ◽  
A.-V. Salsac ◽  
D. Barthès-Biesel
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Cylindrical Tube ◽  
Boundary Integral ◽  
Size Ratio ◽  
Constitutive Law ◽  
Boundary Integral Method ◽  
Flow Strength ◽  
Capsule Deformation

AbstractThe motion and deformation of a spherical elastic capsule freely flowing in a pore of comparable dimension is studied. The thin capsule membrane has a neo-Hookean shear softening constitutive law. The three-dimensional fluid–structure interactions are modelled by coupling a boundary integral method (for the internal and external fluid motion) with a finite element method (for the membrane deformation). In a cylindrical tube with a circular cross-section, the confinement effect of the channel walls leads to compression of the capsule in the hoop direction. The membrane then tends to buckle and to fold as observed experimentally. The capsule deformation is three-dimensional but can be fairly well approximated by an axisymmetric model that ignores the folds. In a microfluidic pore with a square cross-section, the capsule deformation is fully three-dimensional. For the same size ratio and flow rate, a capsule is more deformed in a circular than in a square cross-section pore. We provide new graphs of the deformation parameters and capsule velocity as a function of flow strength and size ratio in a square section pore. We show how these graphs can be used to analyse experimental data on the deformation of artificial capsules in such channels.

Boundary integral equations for magnetic screens in ℝ3

1986 ◽  
Vol 102 (3-4) ◽  
pp. 189-210 ◽  
Author(s):  
Ernst P. Stephan
Keyword(s):  
Integral Equations ◽  
Electromagnetic Waves ◽  
Boundary Integral Equations ◽  
Slight Modification ◽  
Cauchy Data ◽  
Tangential Component ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Optimal Error Estimates ◽  
Exterior Boundary Value Problem

SynopsisA boundary integral method is developed for the scattering of electromagnetic waves at thin obstacles. The exterior boundary value problem for the vector Helmholtz equation with given Neumann data on an open surface piece (screen S) is converted into a system of integral equations for the jumps of the tangential component of the field and its divergence across the screen. A slight modification of the Cauchy data yields a strongly elliptic system of pseudodifferential equations on S which can therefore be used for numerical computations using Galerkin's procedure. The resulting boundary integral equations are analysed using pseudodifferential operator calculus. The principal symbol concept, together with the Wiener–Hopf technique, are used to derive existence and regularity results for the solutions to the boundary integral equations. Quasi-optimal error estimates in the energy norm are given for the numerical scheme.

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