A Hamiltonian description of finite-time singularity in Euler's fluid equations
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Chebyshev solution of large linear systems.
Solution of linear system of equations with singularity and stabile with respect to small changes in matrix elements
LINEAR PROGRAMMING↗
Spaces of type III solutions of the Maxwell- Einstein equations
Type 3 spaces solutions of Maxwell-Einstein equations, examining singular and nonsingular electromagnetic field problems
Cahen, M.↗
Numerical solutions in three dimensional elastostatics
Three dimensional elastostatics problems solution method using singular integral equations solvable numerically for surface tractions and displacements of fully mixed boundary value problem
Cruse, T. A.↗
Theory of radiative transfer in inhomogeneous atmospheres. IV - Application of the matrix perturbation method to a semi-infinite atmosphere
Polarized radiation transfer through inhomogeneous semiinfinite atmosphere by matrix perturbation method, giving nonlinear singular integral equation
Abhyankar, K. D.↗
Elastic cracks and screw dislocation pile-ups crossing a bimaterial interface
Elastic cracks and screw dislocation pile-ups crossing bimaterial interface, deriving dual singular integral equations
Chou, T.-W.↗
Radiation from a parallel-plate waveguide into a dielectric or plasma layer.
An analytical solution for radiation from a truncated parallel-plate waveguide into a dielectric or plasma slab is obtained by solving the Hilbert problem associated with a certain singular integral equation. The technique has the advantage that the edge condition is easily shown to be satisfied, and numerical results can be obtained with excellent accuracy. Numerical results are presented for a variety of dielectric and plasma slabs, parallel-plate separations, and aperture-to-slab distances.
Kostelnicek, R. J.↗
Penny-shaped interface crack between an elastic layer and a half space.
The axially symmetric elastostatic problem for a layer bonded to a half space with different material properties is considered. It is assumed that the bi-material interface contains a penny-shaped crack the surfaces of which are subjected to known tractions. The solution of the problem is reduced to that of a system of singular integral equations of the second kind. A numerical example for an aluminum-epoxy material combination is given. The stress intensity factors and the strain energy release rate are calculated and are given as functions of layer thickness-to-crack radius ratio.
Erdogan, F.↗
A circumferential crack in a cylindrical shell under torsion.
The fully antisymmetric problem for a cylindrical shell with a circumferential crack is considered. The solution of the problem is reduced to that of a system of singular integral equations of the first kind. As an example the torsion of the cylinder is discussed and membrane and bending components of the stress intensity factor ratio are given.
Erdogan, F.↗
The inverse scattering problem at fixed angular momentum for nonlocal separable interactions
The problem of inverse scattering at fixed angular momentum is considered. The problem is particularized to the case of nonlocal separable interactions. A brief survey of the inverse problem for nonlocal separable interactions is presented. This problem can be solved exactly by integration. It amounts to solving singular integral equations of the Hilbert-Mushkhelishvili type, which have been studied extensively in the past and appear in many areas of physics, including theory of elasticity and dispersions relations in high energy physics.
Chadan, K.↗
Bonded half planes containing an arbitrarily oriented crack
The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin transforms, the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given include the stress intensity factors, tHe strain energy release rates, and tHe probable cleavage angles giving the direction of crack propagation.
Erdogan, F.↗
Interaction between parallel cracks in layered composites
The plane strain problem of a multi-layered composite with parallel cracks is considered. The main objective is to study the interaction between parallel and collinear cracks. The problem is formulated in terms of a set of simultaneous singular integral equations which are solved numerically. The effect of material properties on the interaction between cracks is also demonstrated.
Ratwani, M.↗
A penny shaped crack in a filament-reinforced matrix. 2: The crack problem
The elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix was formulated. For a single filament as well as multiple identical filaments located symmetrically around the crack the problem is shown to reduce to a singular integral equation. The solution of the problem is obtained for various geometries and filament-to-matrix stiffness ratios, and the results relating to the angular variation of the stress intensity factor and the maximum filament stress are presented.
Pacella, A. H.↗
Transverse cracks in a strip with reinforced surfaces
The symmetrical problem of two transverse cracks in an elastic strip with reinforced surfaces is formulated in terms of a singular integral equation. The special cases of one central crack or two edge cracks are discussed. Numerical methods for solving the problems with internal cracks are outlined and stress intensity factors are presented for various geometrics and degrees of surface reinforcement.
Krenk, S.↗
Bonded half planes containing an arbitrarily oriented crack
The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin Transforms the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given in the paper include the stress intensity factors, the strain energy release rates, and the probable clevage angles giving the direction of crack propagation.
Erdogan, F.↗
Interaction between parallel cracks in layered composites
The plane strain problem of a millilayered composite with parallel cracks is considered. The main objective is to study the interaction between parallel and collinear cracks. The problem is formulated in terms of a set of simultaneous singular integral equations which are solved numerically. The effect of material properties on the interaction between cracks is also demonstrated.
Ratwani, M.↗
Penny-shaped crack in a fiber-reinforced matrix
Using a slender inclusion model developed earlier, the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles, the problem was reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given, and distribution of the stress intensity factor along the crack border was obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.
Narayanan, T. V.↗
Comparison of some biased estimation methods (including ordinary subset regression) in the linear model
Ridge, Marquardt's generalized inverse, shrunken, and principal components estimators are discussed in terms of the objectives of point estimation of parameters, estimation of the predictive regression function, and hypothesis testing. It is found that as the normal equations approach singularity, more consideration must be given to estimable functions of the parameters as opposed to estimation of the full parameter vector; that biased estimators all introduce constraints on the parameter space; that adoption of mean squared error as a criterion of goodness should be independent of the degree of singularity; and that ordinary least-squares subset regression is the best overall method.
Sidik, S. M.↗