Integral equations for the mixed boundary value problem of a notched elastic half-plane

2015 ◽  
Author(s):  
Maria Yu. Savelyeva ◽  
Yuliya G. Pronina
Keyword(s):  
Boundary Value Problem ◽  
Integral Equations ◽  
Half Plane ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Value Problem

The Problem of Several Indentors Moving on a Viscoelastic Half-Plane

1995 ◽  
Vol 62 (2) ◽  
pp. 380-389 ◽  
Author(s):  
H. Z. Fan ◽  
G. A. C. Graham ◽  
J. M. Golden
Keyword(s):  
Steady State ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Half Plane ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Mixed Boundary Value Problem ◽  
System Of Integral Equations ◽  
Space And Time

The problem of several indentors moving on a viscoelastic half-plane is considered in the noninertial approximation. The solution of this mixed boundary value problem is formulated in terms of a coupled system of integral equations in space and time. These are solved numerically in the steady-state limit for the case of two indentors. The phenomena of hysteretic friction and interaction between the two indentors are explored.

scholarly journals A mixed boundary value problem of a cracked elastic medium under torsion

2021 ◽  
pp. 10-10
Author(s):  
Belkacem Kebli ◽  
Fateh Madani
Keyword(s):  
Boundary Value Problem ◽  
Elastic Medium ◽  
Integral Equations ◽  
Integral Transformation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Crack Problem ◽  
Fredholm Integral Equations ◽  
Mixed Boundary Value Problem ◽  
Penny Shaped Crack

The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material under axisymmetric torsion by a circular rigid inclusion embedded in the elastic medium. With the use of the Hankel integral transformation method, the mixed boundary value problem is reduced to a system of dual integral equations. The latter is converted into a regular system of Fredholm integral equations of the second kind which is then solved by quadrature rule. Numerical results for the displacement, stress and stress intensity factor are presented graphically in some particular cases of the problem.

On a Dirichlet–Neumann–Third mixed boundary value problem for the Helmholtz equation

1983 ◽  
Vol 94 (3-4) ◽  
pp. 221-233 ◽  
Author(s):  
M. David
Keyword(s):  
Boundary Value Problem ◽  
Helmholtz Equation ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Uniqueness Theorems ◽  
Equivalent System ◽  
Mixed Boundary Value Problem ◽  
Existence And Uniqueness Theorems

SynopsisExistence and uniqueness theorems are proved for the solution of a Dirichlet-Neumann-Third mixed boundary value problem for the Helmholtz equation in ℝ3. The proofs make use of an equivalent system of two integral equations of the second kind.

scholarly journals The solution of a mixed boundary value problem in the theory of diffraction by a semi-infinite plane

1975 ◽  
Vol 346 (1647) ◽  
pp. 469-484 ◽  
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Half Plane ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mathematical Problem ◽  
Standard Technique ◽  
Infinite Plane ◽  
Mixed Boundary Value Problem ◽  
Rigid Boundary

A solution is obtained for the problem of the diffraction of a plane wave sound source by a semi-infinite half plane. One surface of the half plane has a soft (pressure release) boundary condition, and the other surface a rigid boundary condition. Two unusual features arise in this boundary value problem. The first is the edge field singularity. It is found to be more singular than that associated with either a completely rigid or a completely soft semi-infinite half plane. The second is that the normal Wiener-Hopf method (which is the standard technique to solve half plane problems) has to be modified to give the solution to the present mixed boundary value problem. The mathematical problem which is solved is an approximate model for a rigid noise barrier, one face of which is treated with an absorbing fining. It is shown that the optimum attenuation in the shadow region is obtained when the absorbing lining is on the side of the screen which makes the smallest angle to the source or the receiver from the edge.

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