scholarly journals RESEARCH OF ACOUSTIC EMISSIONS FROM THE SYSTEM OF COMPLANARY CRACKS

2021 ◽  
Vol 3 (1) ◽  
pp. 45-50
Author(s):  
Olena Stankevych ◽  
◽  
Nazar Stankevych ◽  
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Displacement Field ◽  
Dynamic Problem ◽  
Boundary Integral Equations ◽  
Acoustic Emissions ◽  
Elastic Half Space ◽  
Boundary Integral ◽  
Wave Number ◽  
Coplanar Cracks

The dynamic problem of the displacement field in an elastic half-space caused by the time-steady displacement of the surfaces of the system of disc-shaped coplanar cracks is solved. The solutions are obtained by the method of boundary integral equations. The dependences of elastic displacements on the surface of the half-space on the wave number, the number of defects and the depths of their occurrence are constructed.

scholarly journals Method for solving plane unsteady contact problems for rigid stamp and elastic half-space with a cavity of arbitrary geometry and location

2020 ◽  
Vol 12 (S) ◽  
pp. 99-113
Author(s):  
Yulong LI ◽  
Aron M. ARUTIUNIAN ◽  
Elena L. KUZNETSOVA ◽  
Grigory V. FEDOTENKOV
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Boundary Integral Equations ◽  
Elastic Half Space ◽  
Boundary Integral ◽  
Elastic Plane ◽  
Time Interval ◽  
Arbitrary Geometry ◽  
Rigid Stamp ◽  
Straight Line

In the work, the process of unsteady contact interaction of rigid stamp and elastic half-space having a recessed cavity of arbitrary geometry and location with a smooth boundary was investigated. Three variants of contact conditions are considered: free slip, rigid coupling, and bonded contact. The method for solving the problem is constructed using boundary integral equations. To obtain boundary integral equations, the dynamic reciprocal work theorem is used. The kernels of integral operators are bulk Green functions for the elastic plane. Because of straight-line approximations of the domain boundaries with respect to the spatial variable and straight-line approximations of the boundary values of the desired functions with respect to time, the problem is reduced to solving a system of algebraic equations with respect to the pivotal values of the desired displacements and stresses at each time interval. One of the axes is directed along the regular boundary of half-space, the second - deep into half-space.

Removing Non-Uniqueness in Symmetric Galerkin Boundary Element Method for Elastostatic Neumann Problems and its Application to Half-Space Problems

2020 ◽  
Vol 36 (6) ◽  
pp. 749-761
Author(s):  
Y. -Y. Ko
Keyword(s):  
Boundary Element Method ◽  
Rigid Body ◽  
Boundary Element ◽  
Integral Equations ◽  
Half Space ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Neumann Problems ◽  
Galerkin Boundary Element Method ◽  
Element Method

ABSTRACTWhen the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

scholarly journals Thermomechanical Slip in Elastic Contact Between Identical Materials

2021 ◽  
Vol 15 (4) ◽  
pp. 187-192
Author(s):  
Yurii Streliaiev ◽  
Rostyslav Martynyak ◽  
Kostyantyn Chumak
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Thermal Loading ◽  
Boundary Integral Equations ◽  
Contact Region ◽  
Elastic Half Space ◽  
Boundary Integral ◽  
Subsequent Stage ◽  
Relative Shear ◽  
Increasing Temperature

Abstract The contact problem for interaction between an elastic sphere and an elastic half-space is considered taking into account partial thermomechanical frictional slip induced by thermal expansion of the half-space. The elastic constants of the bodies are assumed to be identical. The Amontons–Coulomb law is used to account for friction. The problem is reduced to non-linear boundary integral equations that correspond to the initial stage of mechanical loading and the subsequent stage of thermal loading. The dependences of the contact stress distribution, relative displacements of the contacting surfaces, dimensions of the stick and slip zones on temperature of the half-space are studied numerically. It was revealed that an increase in temperature causes increases in the shear contact stress and the relative shear displacements of the contacting surfaces. The absolute values of the shear contact stress reach their maximum at the boundaries of the stick zones. The greatest value of the moduli of the relative shear displacements are reached at the boundary of the contact region. The stick zone radius decreases monotonically according to a nonlinear law with increasing temperature.

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