On the Computation of the Stress Intensity Factors in Elastic Plate Flexure Via Boundary Integral Equations

1982 ◽  
pp. 540-553
Author(s):  
J. W. Kim
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Elastic Plate ◽  
Stress Intensity Factors ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Intensity Factors ◽  
Plate Flexure

Scattering by Multiple Crack Configurations

1988 ◽  
Vol 55 (1) ◽  
pp. 104-110 ◽  
Author(s):  
Ch. Zhang ◽  
J. D. Achenbach
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Scattered Field ◽  
Boundary Integral Equations ◽  
Crack Opening ◽  
Boundary Integral ◽  
Intensity Factors ◽  
Closed Crack ◽  
Scattered Fields

A system of boundary integral equations is presented which governs the crack-opening displacements for two-crack configurations. The integral equations are highly singular and they cannot be solved directly by numerical methods. By the approach of this paper the higher order singularities are, however, reduced to integrable singularities, and the integral equations are subsequently discretized and solved numerically. For several configurations numerical results have been obtained for scattered fields and for elastodynamic stress intensity factors. The scattered-field results are interpreted to apply for a partially closed crack as well as for two separate but neighboring cracks. The stress-intensity factors are intended to apply only to the case of separate cracks. The scattered-field results have relevance to the problem of detection and characterization of cracks in the field of quantitative nondestructive evaluation.

Effects of thermal and electric boundary conditions on fracture of three-dimensional thermopiezoelectric media

2017 ◽  
Vol 29 (6) ◽  
pp. 1255-1271 ◽  
Author(s):  
MingHao Zhao ◽  
Yuan Li ◽  
CuiYing Fan
Keyword(s):  
Stress Intensity ◽  
Boundary Conditions ◽  
Stress Intensity Factors ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Displacement Discontinuity ◽  
Green Functions ◽  
Intensity Factors

An arbitrarily shaped planar crack under different thermal and electric boundary conditions on the crack surfaces is studied in three-dimensional transversely isotropic thermopiezoelectric media subjected to thermal–mechanical–electric coupling fields. Using Hankel transformations, Green functions are derived for unit point extended displacement discontinuities in three-dimensional transversely isotropic thermopiezoelectric media, where the extended displacement discontinuities include the conventional displacement discontinuities, electric potential discontinuity, as well as the temperature discontinuity. On the basis of these Green functions, the extended displacement discontinuity boundary integral equations for arbitrarily shaped planar cracks in the isotropic plane of three-dimensional transversely isotropic thermopiezoelectric media are established under different thermal and electric boundary conditions on the crack surfaces, namely, the thermally and electrically impermeable, permeable, and semi-permeable boundary conditions. The singularities of near-crack border fields are analyzed and the extended stress intensity factors are expressed in terms of the extended displacement discontinuities. The effect of different thermal and electric boundary conditions on the extended stress intensity factors is studied via the extended displacement discontinuity boundary element method. Subsequent numerical results of elliptical cracks subjected to combined thermal–mechanical–electric loadings are obtained.

scholarly journals Dynamic stress intensity factors of interacting branched cracks

2019 ◽  
Vol 285 ◽  
pp. 00004
Author(s):  
Piotr Fedeliński
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Numerical Solutions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Inversion Method ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Element Method

In the present work the boundary element method (BEM) is applied to analysis of statically and dynamically loaded infinite plates with multiple stationary branched cracks. The material of the plates is linear-elastic, homogenous and isotropic. In the applied BEM approach the displacement and traction boundary integral equations are used simultaneously for nodes on crack surfaces. Contrary to the finite element method (FEM) in the BEM numerical solutions are obtained by discretization of external boundaries and crack surfaces. The dynamic problem is solved by using the Laplace transform method and the solution in the time domain is computed by the Durbin numerical inversion method. Numerical examples of multiple branched cracks in infinite plates subjected to static and dynamic loadings are presented. An influence of orientation, distances between cracks and the number of cracks on static and dynamic stress intensity factors (SIF) is studied.

Analysis of Crack Propagation in Roller Bearings Using the Boundary Integral Equation Method—A Mixed-Mode Loading Problem

1988 ◽  
Vol 110 (3) ◽  
pp. 408-413 ◽  
Author(s):  
L. J. Ghosn
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Crack Propagation ◽  
Boundary Integral Equation ◽  
Stress Intensity Factors ◽  
High Speed ◽  
Roller Bearing ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Intensity Factors

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

The Sound Transmission Through a Baffled, Thin, Finite, Elastic Plate by Using Boundary Integral Equations

1999 ◽  
Author(s):  
Yasuhito Kawai
Keyword(s):  
Integral Equations ◽  
Elastic Plate ◽  
Boundary Integral Equations ◽  
Sound Transmission ◽  
Coupled System ◽  
Boundary Integral ◽  
Image Method ◽  
Thin Elastic Plate ◽  
Control Engineering ◽  
Sound Fields

Abstract The prediction of sound transmission through a thin elastic plate such as a window is an important problem in the field of noise control engineering. Integral equations which express sound fields in infinite half spaces which are divided off by the baffle and the elastic plate are introduced and combined with the equation of plate vibration to solve as a coupled system. The image method is used in every equation to reduce unknown functions and boundaries which should be considered. Some numerical examples are solved numerically to examine the method.

Stress Intensity Factors of Multiple Cracked Sheet With Riveted Stiffeners

1991 ◽  
Vol 113 (3) ◽  
pp. 280-284 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Intensity Factors ◽  
Single Crack ◽  
Numerical Examples ◽  
Unknown Density

A new method is proposed for analyzing the stress intensity factors of multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown density of surface tractions and fastener forces, Fredholm integral equations and compatibility equations of displacements among the sheet, fasteners, and stiffeners are formulated. After solving the unknown density, the stress intensity factors of multiple cracks in the sheet are determined. Some numerical examples are analyzed.

scholarly journals Boundary Integral Equations for an Anisotropic Bimaterial with Thermally Imperfect Interface and Internal Inhomogeneities

2016 ◽  
Vol 10 (1) ◽  
pp. 66-74 ◽  
Author(s):  
Heorhiy Sulym ◽  
Iaroslav Pasternak ◽  
Mykhailo Tomashivskyy
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Imperfect Interface ◽  
Boundary Integral ◽  
Bimaterial Interface ◽  
Intensity Factors ◽  
New Approach ◽  
Adhesive Layers ◽  
Type Integral ◽  
Anisotropic Bimaterial

Abstract This paper studies a thermoelastic anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities. Based on the complex variable calculus and the extended Stroh formalism a new approach is proposed for obtaining the Somigliana type integral formulae and corresponding boundary integral equations for a thermoelastic bimaterial consisting of two half-spaces with different thermal and mechanical properties. The half-spaces are bonded together with mechanically perfect and thermally imperfect interface, which model interfacial adhesive layers present in bimaterial solids. Obtained integral equations are introduced into the modified boundary element method that allows solving arbitrary 2D thermoelacticity problems for anisotropic bimaterial solids with imperfect thin thermo-resistant inter-facial layer, which half-spaces contain cracks and thin inclusions. Presented numerical examples show the effect of thermal resistance of the bimaterial interface on the stress intensity factors at thin inhomogeneities.

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