Basic Boundary Value Problems Research Articles

Wave Propagation on the Boundary Plane of an Anisotropic Body with Inclined Anisotropic Principle Axis.

In this paper, SH (horizontally polarized shear) wave propagation in an inclined anisotropic elastic body is investigated. It is analyzed as a basic boundary value problem as the interface between an inclined anisotropic half space and an isotropic half space. Direction of wave propagation is determined by the use of power flow density. It is shown that power flow density determines the direction of the principle axis of an inclined anisotropic body. Reflection and transmission coefficients in the interface are also discussed. The reflection coefficient in the interface is large when inclined angle in large.

Extensions of the closed form method for substrate thermal analyzers to include thermal resistances from source-to-substrate and source-to-ambient

The Fourier series/integral closed-form method for substrate thermal analyzers has been limited by the specification of heat sources on the substrate surface. A method of complementing the basic substrate boundary value problem with lumped thermal resistances is described. In this manner, the thermal interface resistance between a chip package and board, as well as between the same package and a local ambient can be accommodated. The technique consists of combining the methods of Fourier series solution and lumped parameter thermal resistances. The theory is verified by comparing results with both thermal network and finite element model calculations for a sample problem consisting of four active devices attached to a substrate. The ramifications of a uniform heat flux at the board surface are examined by evaluating an approximate representation of a surface mount chip package. Results are compared with experimental test data for a small printed circuit board with 56 dual in-line resistor packs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Some basic boundary value problems of thermoelasticity for a prolate spheroid

Some basic boundary value problems of thermoelasticity for a prolate spheroid

The equation [formula omitted] and several problems associated with it

A fundamental solution of the equation in the title has been found. The existence of a phenomenon of the “wave front” type has been established on the basis of this solution and basic initial value and boundary value problems for this equation have also been investigated.

Numerical solution of boundary value problems for fourth-order elliptic equations

Iterative methods for the numerical solution of the basic boundary value problems for the biharmonic equation in the plane are considered. The method of fictitious domains is used to solve the Dirichlet problem in an irregular domain. The results of computations for some model problems are given.

A finite element analysis for elastoplastic bodies obeying Hencky's law

Using the Haar-Kármán principle, approximate solutions of the basic boundary value problems are proposed and studied, which consist of piecewise linear stress fields on composite triangles. The torsion problem is solved in an analogous manner. Some convergence results are proven.

On the convex functionals analogous to the generalized trefftz functionals in variational problems of the theory of elasticity

A possible general approach for constructing convex functionals in the variational problems of the theory of elasticity, utilizing the Lagrange's multipliers, is indicated. It is shown that such functionals can be constructed in exactly the same manner as the generalized Trefftz functionals which were constructed in /1/ for the basic boundary value problems of the theory of elasticity. The problem of minimizing such functionals using the concept of duality is also discussed.

ON THE ASYMPTOTIC BEHAVIOR, FOR LARGE VALUES OF THE TIME, OF SOLUTIONS OF EXTERIOR BOUNDARY VALUE PROBLEMS FOR THE WAVE EQUATION WITH TWO SPACE VARIABLES

Waves are constructed which characterize the behavior, for large values of time , of the Green's functions of the basic exterior boundary value problems for the wave equation with two space variables (behind the wave front). Representations of the Green's functions (and the solutions) are obtained in the form of series, asymptotic in as . The principle of limiting amplitude is proved, i.e., the existence of the limit is established for solutions of the basic exterior boundary value problems for the wave equation in the case of a time-periodic driving force (), and a representation is obtained for the difference in the form of a series asymptotic in as ; it is shown that the rate of emergence of a solution to a periodic regime cannot be greater than a power of .Bibliography: 18 titles.

The influence of the atmosphere on geoid and potential coefficient determinations from gravity data

For the precise computation of geoid undulations the effect of the attraction of the atmosphere on the solution of the basic boundary value problem of gravimetric geodesy must be considered. This paper extends the theory of Moritz for deriving an atmospheric correction to the case when the undulations are computed by combining anomalies in a cap surrounding the computation point with information derived from potential coefficients. The correction term is a function of the cap size and the topography within the cap. It reaches a value of 3.0 m for a cap size of 30 deg, variations on the decimeter level being caused by variations in the topography. The effect of the atmospheric correction terms on potential coefficients is found to be small, reaching a maximum of 0.0055 millionths at n = 2, m = 2 when terrestrial gravity data are considered. The magnitude of this correction indicates that in future potential coefficient determination from gravity data the atmospheric correction should be made to such data.

Singular integral equations in elastic dielectrics

Galerkin representations for the displacement vector, polarization vector and the potential field are obtained by elementary matrix inversions of the equations of equilibrium. Matrices of fundamental solutions of an infinite elastic dielectric continuum subjected to a concentrated body force, an electric force, and a charge density, are constructed. Theorems are proved on the discontinuity of double layer potentials and R, M, M operators of single layer potentials. By means of these theorems, the solution of the two basic boundary value problems has been reduced to the solution of a system of seven singular integral equations.

Singular integral equations in asymmetric thermoelasticity

Integral representations for the displacement vector, rotation vector and the temperature have been constructed by making use of the three basic singular solutions in asymmetric thermoelasticity. The potentials of a single and double layer have been constructed. The solution of the basic boundary value problems has been reduced to the solution of a system of seven singular integral equations by utilizing the theorems proved on the discontinuities of the double layer potentials and P (stress), M (couple-stress) and ∂/∂n operators of the single layer potentials.

The general and basic boundary value problems of plane steady jet flows and the corresponding nonlinear equations

The general boundary value problem, including known plane steady jet flows of an ideal incompressible fluid, is formulated. The simplest problem retaining all the specific features of the general problem, known as the basic problem, is separated from the general problem. The solution of the basic problem is reduced to solving a non-linear integro-differential equation and also to solving nonlinear integral equations. Examples of flows whose determination is reduced to' solving the basic problem are cited.

Radiation from a sphere in compressible plasma

The Hansen's vector wave functions have been modified so it could apply directly for the solution of general exterior boundary value problems in compressible plasma for a spherical geometry. The vector wave functionL has been included to represent an acoustic wave and the three angular orthogonal functions have been defined using complex Fourier series in the azymuthal direction. Using this modified method of vector wave functions, the exterior spherical boundary value problem in compressible isotropic plasma has been solved. The boundary conditions prescribed over the surface of the sphere have been the tangential electric field (or the tangential magnetic field) and the radial component of the velocity vector (or the pressure). From those four basic boundary value problems the coefficients have been derived and several particular cases has been discussed.

Initial-value methods for the basic boundary-value problem and integral equation of radiative transfer

We consider the problem of radiative transfer in a plane-parallel atmosphere which absorbs radiation and scatters it isotropically, there being a continuous distribution of primary internal sources of radiation. Our aim is to produce an effective numerical technique for calculating the internal intensity and the source functions. A major consideration is the computer's ability to solve initial-value problems for large systems of ordinary differential equations. We derive new differential-integral equations for the internal intensity at a fixed point and direction, and the source function at a fixed point, the new independent variable being the thickness of the atmosphere. Using standard quadrature techniques, we approximate these equations by systems of ordinary differential equations whose numerical treatment is straightforward. This work may be viewed as a new approach to the study of integral equations and linear unstable two-point boundary-value problems.

On the Integral Equations of the Basic Boundary Value Problems of Elasticity of Inhomogeneous Media

On the Integral Equations of the Basic Boundary Value Problems of Elasticity of Inhomogeneous Media

Schauder estimates under incomplete Hölder continuity assumptions

Abstract : The possibility of obtaining a priori pointwise estimates involving Holder difference quotients is explored with respect to some of the independent variables. The first step is the derivation of certain potential theoretic results. These are applied to functions given convolutions with a fundamental solution to an elliptic operator as kernel, and to solutions of the basic boundary value problem with compact support when the operators have constant coefficients and the domain is a half-space. The results are extended to a class of problems with variable coefficients and domains with curved boundaries. (Author)