scholarly journals Doubly Periodic Cracks in the Anisotropic Medium with the Account of Contact of Their Faces

2014 ◽  
Vol 8 (3) ◽  
pp. 160-164 ◽  
Author(s):  
Olesya Maksymovych ◽  
Iaroslav Pasternak ◽  
Heorhiy Sulym ◽  
Serhiy Kutsyk
Keyword(s):  
Complex Variable ◽  
Boundary Integral Equations ◽  
Solution Procedure ◽  
Boundary Integral ◽  
Singular Boundary ◽  
Anisotropic Elastic Medium ◽  
Periodic Cracks ◽  
Anisotropic Elastic ◽  
Crack Faces ◽  
Integral Formulae

Abstract The paper presents complex variable integral formulae and singular boundary integral equations for doubly periodic cracks in anisotropic elastic medium. It utilizes the numerical solution procedure, which accounts for the contact of crack faces and produce accurate results for SIF evaluation. It is shown that the account of contact effects significantly influence the SIF of doubly periodic curvilinear cracks both for isotropic and anisotropic materials.

Analysis of Cracks in Functionally Graded Piezoelectric Materials by a Frequency-Domain BEM

2017 ◽  
Vol 754 ◽  
pp. 149-152
Author(s):  
Michael Wünsche ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Ch. Zhang ◽  
M. Repka
Keyword(s):  
Frequency Domain ◽  
Boundary Integral Equations ◽  
Piezoelectric Materials ◽  
Domain Boundary ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Functionally Graded ◽  
Singular Boundary ◽  
Square Root ◽  
Functionally Graded Piezoelectric Materials

Time-harmonic crack analysis in two-dimensional piezoelectric functionally graded materials (FGMs) is presented in this paper. A frequency-domain boundary element method (BEM) is developed for this purpose. Since fundamental solutions for piezoelectric FGMs are not available, a boundary-domain integral formulation is derived. This requires only the frequency-domain fundamental solutions for homogeneous piezoelectric materials. The radial integration method is adopted to compute the resulting domain integrals. The collocation method is used for the spatial discretization of the frequency-domain boundary integral equations. Adjacent the crack-tips square-root elements are implemented to capture the local square-root-behavior of the generalized crack-opening-displacements properly. Special regularization techniques based on a suitable change of variables are used to deal with the singular boundary integrals. Numerical examples will be presented and discussed to show the influences of the material gradation and the dynamic loading on the intensity factors.

scholarly journals NONLINEAR PROBLEM OF FRACTURE MECHANICS OF AN INTERFACE CRACK SUBJECTED TO SHEAR WAVE

2021 ◽  
pp. 55-64
Author(s):  
Oleksandr Menshykov ◽  
Vasyl Menshykov ◽  
Olga Kladova
Keyword(s):  
Stress Intensity ◽  
Fracture Mechanics ◽  
Integral Equations ◽  
Shear Wave ◽  
Contact Zone ◽  
Interface Crack ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Contact Boundary ◽  
Crack Faces

Solution for the problem for an interface crack under the action of a harmonic shear wave in normal direction is presented. The contact of the crack faces is put into consideration. The problem is solved by the boundary integral equations method, the vector components in the boundary integral equations are presented by Fourier series. The unilateral Signorini boundary conditions are involved to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone. Amonton-Coulomb Friction Law included allows to put into consideration relative resting of the crack opposite faces or their relative motion when one crack face is slipping or sliding across another face. The contact boundary restrictions are implemented using the iterative correction algorithm. The mathematical model adequacy is checked by comparing with classical model solution for statics problems that takes into account the crack faces contact. Numerical researches of friction influence on the displacement and contact forces distribution, size of contact zone are carried out. Influence of the faces contact and value of the friction coefficient on the distribution of stress intensity coefficients of normal rupture and transverse shear, which are the parameters of the biomaterial fracture, are presented and analyzed. It is shown that the nature of change in the distribution of the stress intensity coefficients for the conditions of tensile and shear waves is fundamentally different. It is concluded that it is possible to extend the approach proposed to the problems of three-dimensional fracture mechanics for composites with interfacial cracks at arbitrary dynamic loading.

A Complex Variable Boundary Element-Free Method for Potential and Helmholtz Problems in Three Dimensions

2019 ◽  
Vol 17 (02) ◽  
pp. 1850129 ◽  
Author(s):  
Xiaolin Li ◽  
Shougui Zhang ◽  
Yan Wang ◽  
Hao Chen
Keyword(s):  
Boundary Element ◽  
Complex Variable ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Variable Boundary ◽  
Current Implementation ◽  
Element Free Method ◽  
Element Free ◽  
3D Surfaces

The complex variable boundary element-free method (CVBEFM) is a meshless method that takes the advantages of both boundary integral equations (BIEs) in dimension reduction and the complex variable moving least squares (CVMLS) approximation in element elimination. The CVBEFM is developed in this paper for solving 3D problems. This paper is an attempt in applying complex variable meshless methods to 3D problems. Formulations of the CVMLS approximation on 3D surfaces and the CVBEFM for 3D potential and Helmholtz problems are given. In the current implementation, the CVMLS shape function of 3D problems is formed with 1D basis functions, and the boundary conditions in the CVBEFM can be applied directly and easily. Some numerical examples are presented to demonstrate the method.

A New Boundary Integral Equation Formulation for Elastodynamic and Elastostatic Crack Analysis

1989 ◽  
Vol 56 (2) ◽  
pp. 284-290 ◽  
Author(s):  
Ch. Zhang ◽  
J. D. Achenbach
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Crack Opening ◽  
Boundary Integral ◽  
Static Case ◽  
Dislocation Densities ◽  
Integral Equation Formulation ◽  
Conventional Manner ◽  
Crack Faces ◽  
Natural Way

An elastodynamic conservation integral, the J˜k integral, is employed to derive boundary integral equations for crack configurations in a direct and natural way. These equations immediately have lower-order singularities than the ones obtained in the conventional manner by the use of the Betti-Rayleigh reciprocity relation. This is an important advantage for the development of numerical procedures for solving the BIE’s, and for an accurate calculation of the strains and stresses at internal points close to the crack faces. For curved cracks of arbitrary shape the BIE’s presented here have simple forms, and they do not require integration by parts, as in the conventional formulation. For the dynamic case the unknown quantities are the crack opening displacements and their derivatives (dislocation densities), while for the static case only the dislocation densities appear in the formulation. For plane cracks the boundary integral equations reduce to the ones obtained by other investigators.

scholarly journals Low Frequency Sloshing Analysis of Cylindrical Containers with Flat and Conical Baffles

2017 ◽  
Vol 22 (4) ◽  
pp. 867-881 ◽  
Author(s):  
V. Gnitko ◽  
Y. Naumemko ◽  
E. Strelnikova
Keyword(s):  
Velocity Potential ◽  
Boundary Integral Equations ◽  
Low Frequency ◽  
Boundary Integral ◽  
Boundary Element Methods ◽  
Singular Boundary ◽  
Circular Plates ◽  
Compound Shell ◽  
Container Model ◽  
Compound Shell Of Revolution

Abstract This paper presents an analysis of low-frequency liquid vibrations in rigid partially filled containers with baffles. The liquid is supposed to be an ideal and incompressible one and its flow is irrotational. A compound shell of revolution is considered as the container model. For evaluating the velocity potential the system of singular boundary integral equations has been obtained. The single-domain and multi-domain reduced boundary element methods have been used for its numerical solution. The numerical simulation is performed to validate the proposed method and to estimate the sloshing frequencies and modes of fluid-filled cylindrical shells with baffles in the forms of circular plates and truncated cones. Both axisymmetric and non-axisymmetric modes of liquid vibrations in baffled and un-baffled tanks have been considered. The proposed method makes it possible to determine a suitable place with a proper height for installing baffles in tanks by using the numerical experiment.

scholarly journals METHOD OF GENERALIZED FUNCTIONS IN PLANE BOUNDARY VALUE PROBLEMS OF UNCOUPLED THERMOELASTODYNAMICS

2021 ◽  
Author(s):  
Assiyat Dadayeva ◽  
Lyudmila Alexeyeva
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Generalized Functions ◽  
Boundary Integral ◽  
Generalized Solutions ◽  
Plane Boundary ◽  
Unknown Boundary ◽  
Singular Boundary

Nonstationary boundary value problems of uncoupled thermoelasticity are considered. A method of boundary integral equations in the initial space-time has been developed for solving boundary value problems of thermoelasticity by plane deformation. According to generalized functions method the generalized solutions of boundary value problems are constructed and their regular integral representations are obtained. These solutions allow, using known boundary values and initial conditions (displacements, temperature, stresses and heat flux), to determine the thermally stressed state of the medium under the influence of various forces and thermal loads. Resolving singular boundary integral equations are constructed to determine the unknown boundary functions.

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