System Of Dual Equations Research Articles

Discretization and Numerical Solution of a Plane Problem in the Mechanics of Interfacial Cracks

The Fourier transform is used to reduce the linear plane problem of the tension of a body with an interfacial crack to a system of dual equations for the transformed stresses and, then, to a system of integro-differential equations for the difference of displacements of the crack faces. After discretization, this latter system transforms into a system of algebraic equations for displacements of the crack faces. The effect of the bielastic constant and the number of discretization points on the half-length of the crack faces and the distribution of stresses at the interface is studied

Solvability of Some Classes of Systems of Dual Integral Equations Involving Fourier Transforms

The aim of the present work is to consider the existence and uniqueness problems for some classes of general systems of dual integral equations involving Fourier transforms of generalized functions, which are a generalization of some systems of dual equations encountered in the mixed boundary value problems of mathematical physics and contact problems of elasticity.

Accurate evaluation of the electric polarizability of a small hole in a thick conducting wall

Many boundary-value problems have been formulated as a system of dual integral equations, and the mathematical treatment of such equations is well known. This paper presents a procedure for reformulating a static problem involving a thick structure as a system of dual equations, whose solution is evaluated by means of a Neumann series.

High-frequency surface currents induced on a spherical reflector by the edge-diffraction of obliquely incident waves

An explicit expression of the high-frequency surface current excited on a perfectly conducting spherical cap by the edge-diffraction of an obliquely incident wave is derived. The result is given in the GTD terminology and shows the influence of the incidence angles on the transfer functions. To this end the real (physical) space is embedded into a twofold extended abstract space in which an equivalent canonical problem is established. This latter yields a system of dual integral equations whose kernels were not previously treated. By inverting these new kernels, the system of dual equations is reduced to two independent Wiener-Hopf problems. From the asymptotic solutions of these problems, one derives the expression of the edge-excited current along with the known geometrical optics term. The resutlt can be used directly in practical applications. If the incident ray becomes normal to the edge, then the resulting expressions are reduced to the already known expressions. The basic idea and general formulas used here can also be used to solve other diffraction problems with similar geometry.