On a boundary-value problem connected with the reaction of a half-space to a short laser pulse

1997 ◽  
Vol 52 (2) ◽  
pp. 400-401
Author(s):  
G Fichera
Keyword(s):  
Laser Pulse ◽  
Boundary Value Problem ◽  
Half Space ◽  
Boundary Value ◽  
Short Laser Pulse

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

scholarly journals NUMERICAL MODELLING OF DYNAMIC RESPONSE OF A PARTIALLY SATURATED POROELASTIC HALF-SPACE IN CASE OF A LOAD ACTING INSIDE A CUBIC CAVITY

2020 ◽  
Vol 82 (4) ◽  
pp. 507-523
Author(s):  
A.N. Petrov ◽  
M.V. Grigoryev
Keyword(s):  
Boundary Value Problem ◽  
Half Space ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Boundary Integral ◽  
Poroelastic Medium ◽  
Partially Saturated ◽  
Pore Pressures ◽  
The Laplace Transform ◽  
Poroelastic Material

Computer modeling based on the boundary element method is performed for the problem of loading in terms of the Heaviside step function inside a cubic cavity located in a partially saturated poroelastic half-space. A poroelastic medium is represented by a heterogeneous material-based model consisting of an elastic matrix phase and two phases of fillers – liquid and gas filling the pore system. The material model corresponds to a three-component medium. The constitutive relations of poroelastic medium written in terms skeleton displacements and pore pressures of fillers are considered. The original initial-boundary value problem is reduced to a boundary value problem by using the formal application of the Laplace transform. The research technique is based on the direct approach boundary integral equations of 3D isotropic linear theory of poroelasticity. Boundary integral equations corresponding to the boundary value problem are solved by the boundary element method in combination with the collocation method. In this study 8-noded elements have been adopted to discretize the boundary of poroelastic half-space. It is assumed that the element is linear with respect to displacements and pore pressures, while only one central node is used to represent tractions and fluxes. Algorithms for eliminating singularities, decreasing the order and subdividing elements are employed to compute the integral coefficients of a discrete analogue of the boundary integral equation. Regular integrals are calculated using the Gauss quadrature formula. The solution in time is obtained by numerical inversion of the Laplace transform. The numerical inversion method relies on quadrature formulas for computing the convolution integral. The time dependences of unknown displacement functions and pore pressures at points on the surface of the half-space and the cavity are plotted. The corresponding graphs are given. The influence of the cavity depth and degree of saturation on dynamic responses is investigated. The solution obtained by using the model of a fully saturated poroelastic material is compared to that of partially saturated poroelastic material. It is noted that the model used for solving this problem leads to an underestimation of displacement and overestimation of pore pressure estimates.

scholarly journals A BOUNDARY VALUE PROBLEM FOR DEGENERATIVE SYSTEMOFEQUATIONS OFBITSADZE – YANUSHAUSKAS

2017 ◽  
Vol 18 (3.1) ◽  
pp. 14-19
Author(s):  
I.M. Abdrakhmanov ◽  
R.P. Abdrakhmanova
Keyword(s):  
Boundary Value Problem ◽  
Half Space ◽  
Boundary Value ◽  
Dimensional System ◽  
Elliptic Type

In the article, a boundary value problem for a singular many-dimensional system of elliptic type equations in half-space is considered.

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