Calculation of weight functions for three-dimensional bodies with cracks

1989 ◽  
Vol 21 (11) ◽  
pp. 1474-1480
Author(s):  
G. P. Nikishkov ◽  
T. A. Chernysh
Keyword(s):  
Three Dimensional ◽  
Weight Functions

Weight Functions for Three-Dimensional Symmetrical Crack Problems

2009 ◽  
pp. 448-448-23 ◽  
Author(s):  
RC Labbens ◽  
J Heliot ◽  
A Pellissier-Tanon
Keyword(s):  
Three Dimensional ◽  
Weight Functions ◽  
Crack Problems

ON THE PROBLEM OF RESTORING A FUNCTION IN THREE DIMENSIONAL SPACE BY THE FAMILY OF CONES

2021 ◽  
Vol 10 (11) ◽  
pp. 3505-3513
Author(s):  
Z.Kh. Ochilov ◽  
M.I. Muminov
Keyword(s):  
Weight Function ◽  
Exact Solutions ◽  
Special Form ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Weight Functions ◽  
The Family ◽  
The Given ◽  
Three Dimensional Space

In this paper, we consider the problem of recovering a function in three-dimensional space from a family of cones with a weight function of a special form. Exact solutions of the problem are obtained for the given weight functions. A class of parameters for the problem that has no solution is constructed.

Square Cracks in Three-Dimensional Transversely Isotropic Solids

2012 ◽  
Vol 487 ◽  
pp. 617-621
Author(s):  
Ya Dong Bian ◽  
Yu Zhou Sun
Keyword(s):  
Crack Opening ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Least Square ◽  
Weight Functions ◽  
Opening Displacement ◽  
Moving Least Square ◽  
Moving Least Square Approximation ◽  
Fracture Damage

This paper presents a study for the square crack in a three-dimensional infinite transversely isotropic medium, which can model the fracture damage of rock that displays transversely isotropic behavior. The study is based on a newly derived boundary integral equation. To carry out the numerical simulation, the crack opening displacement is first expressed as the product of the weight functions and the characteristic terms, and the unknown weight is approximated with the moving least-square approximation. A boundary type numerical scheme is established, and the effect of the orientation of the principle axis on the stress intensity factor is studied. The interaction between two coplanar square cracks are also modeled and discussed.

scholarly journals THREE-DIMENSIONAL DENSITY MODEL OF THE EARTH’S CRUST OF THE TERRITORY OF THE REPUBLIC OF NIGER

2021 ◽  
pp. 6-21
Author(s):  
V.N. Glaznev ◽  
◽  
M.V. Mints ◽  
I.A. Yakuba ◽  
◽  
...  
Keyword(s):  
Gravity Field ◽  
Three Dimensional ◽  
Earth’S Crust ◽  
Density Model ◽  
Weight Functions ◽  
Rift System ◽  
Data Set ◽  
Anomalous Gravity ◽  
The Republic ◽  
Earth's Crust

The paper considers the results of calculation of the three-dimensional density model of the Earth’s crust for the territory of the Republic of Niger in conditions of incomplete initial geological and geophysical information. A brief description of the geological structure of the research region is given and the task of the study is formulated. The initial data set of density modeling is described, including: the anomalous gravity field, the initial model of the medium, the constraints on the desired solution, and the weight functions of redistribution of field incompatibilities. Inversion of the anomalous gravity field was performed in a three-dimensional formulation for a regular grid with a 25×25 km spacing in the plan and 14 layers of irregular vertical grid. The density model of the crystalline crust obtained by solving the inverse problem was combined with a priori data on the density of the upper mantle layer and the previously constructed layered model of the sedimentary cover of the region. The main features of the density model of the Earth’s crust are considered and its density heterogeneities are compared with the regional geological and tectonic data. The leading role of young structures of the West African rift System and their relationship with density inhomogeneities in the lower and middle crust of the territory of the Republic of Niger was noted.

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