scholarly journals Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nyurgun Lazarev
Keyword(s):  
Inverse Problem ◽  
Interfacial Crack ◽  
Variational Problems ◽  
Elastic Media ◽  
Displacement Boundary ◽  
Joint Point ◽  
The Family ◽  
Crack Faces ◽  
Inequality Type ◽  
Passage To The Limit

AbstractWe consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacial crack between the inclusions and the surrounding elastic media. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. The problems of the family depend on a parameter specifying the coordinate of a connection point of the inclusions. For the considered family of problems, we formulate a new inverse problem of finding unknown coordinates of a hinge joint point. The continuity of solutions of the problems on this parameter is proved. The solvability of this inverse problem has been established. Using a passage to the limit, a qualitative connection between the problems for plates with flat and bulk hinged inclusions is shown.

Junction problem for rigid and Timoshenko elastic inclusions in elastic bodies

2015 ◽  
Vol 22 (4) ◽  
pp. 737-750 ◽  
Author(s):  
AM Khludnev ◽  
L Faella ◽  
TS Popova
Keyword(s):  
Rigid Inclusion ◽  
Existence Of Solutions ◽  
Elastic Inclusion ◽  
Joint Point ◽  
Elastic Bodies ◽  
Rigidity Parameter ◽  
Elastic Inclusions ◽  
Type Boundary ◽  
Crack Faces ◽  
Inequality Type

This paper concerns an equilibrium problem for a two-dimensional elastic body with a thin Timoshenko elastic inclusion and a thin rigid inclusion. It is assumed that the inclusions have a joint point and we analyze a junction problem for these inclusions. The existence of solutions is proved and the different equivalent formulations of the problem are discussed. In particular, the junction conditions at the joint point are found. A delamination of the elastic inclusion is also assumed. In this case, the inequality-type boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. We investigate the convergence to infinity and zero of a rigidity parameter of the elastic inclusion. It is proved that in the limit, we obtain a rigid inclusion and a zero rigidity inclusion (a crack).

Mutual influence of the faces contact area and the pre-fracture zone near the tip of the interfacial crack

2020 ◽  
Vol 13 (3) ◽  
pp. 143-161
Author(s):  
M.V. Dudyk
Keyword(s):  
Contact Area ◽  
Fracture Zone ◽  
Mutual Influence ◽  
Interfacial Crack ◽  
Normal Displacement ◽  
Crack Model ◽  
Hopf Equation ◽  
Resistant Material ◽  
Order Of Magnitude ◽  
Crack Faces

BACKGROUND: Under plane strain conditions, a crack model was developed on a plane interface between two different materials, which assumes the existence near its tip of the faces contact area and a narrow lateral pre-fracture zone in a less crack-resistant material of the composite compound. The pre-fracture zone is modeled by the line of normal displacement rupture, on which the normal stress is equal to the tensile strength of the material. Assuming that the dimensions of the pre-fracture zone and the contact zone have the same order of magnitude and are significantly smaller than the crack length, the problem is reduced to the vector Wiener–Hopf equation. METHODS: An approximate method for solving the vector Wiener–Hopf equation was developed, which was used to obtain the equations for determining the sizes of the pre-fracture zone and the contact faces area. The pre-fracture zone orientation was determined from the condition of the potential energy maximum accumulated in the zone. Numerical calculations of the indicated parameters and analysis of their dependences on the configuration and module of external load are executed. RESULTS: A significant mutual influence of the pre-fracture zone and crack faces contact on their sizes and orientation of the zone was revealed.

Analysis of a Heat Flux over a Region with a Crack near a Rigid Inclusion

2010 ◽  
Vol 163-167 ◽  
pp. 4482-4485
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Heat Flux ◽  
Rigid Inclusion ◽  
Mapping Function ◽  
Function Technique ◽  
Uniform Heat Flux ◽  
Principle Of Superposition ◽  
Rational Mapping ◽  
Displacement Boundary ◽  
Crack Tips ◽  
Crack Faces

The thermoelastic problem of a heat flux over a region with a crack near a rigid inclusion is studied. The inclusion is assumed fixed, which implies the translation and the rotation are restrained. The crack faces are assumed free of stress. Both of the inclusion and the crack are under thermal adiabatic condition. In the analysis, the original problem was reduced to a series of displacement boundary value problems by using the principle of superposition. The Green’s function method is used to obtain the solution of the prescribed problem in the forms of integral equations. The basic problems therefore become those for an edge dislocation, and for a heat source couple, as well as the problem of a plane containing the inclusion under a uniform heat flux. These problems are solved using the complex variable method along with the rational mapping function technique. The variations of the stress intensity factors at the crack tips with various crack lengths and heat flux angles are shown. The effects of the inclusion shape and size are also investigated.

An Inverse Problem Associated With Modification of Incomplete Dynamic Systems

1991 ◽  
Vol 58 (1) ◽  
pp. 233-237 ◽  
Author(s):  
Y. M. Ram ◽  
S. G. Braun
Keyword(s):  
Inverse Problem ◽  
Dynamic Systems ◽  
Best Approximation ◽  
Natural Frequencies ◽  
Linear Structure ◽  
Vibration Test ◽  
Natural Frequencies And Modes ◽  
The Best Approximation ◽  
Stiffness Matrices ◽  
The Family

Given an incomplete set of natural frequencies and modes of a linear structure from a vibration test, the problem of computing the necessary changes in the structure to reach a desired spectra is considered. A criterion of optimality which gives the best approximation from a certain subspace is formulated. Then formulae for evaluating the family of all mathematical solutions are given, resulting in a class of mathematical incremental mass and stiffness matrices. Finally, we describe the problem of the realization of the mathematical solutions by constructing a model of a given type.

scholarly journals Fictitious Domain Method for Equilibrium Problems of the Kirchhoff-Love Plates with Nonpenetration Conditions for Known Configurations of Plate Edges

2019 ◽  
pp. 674-686
Author(s):  
Nyurgun P. Lazarev ◽  
Vladimir V. Everstov ◽  
Natalya A. Romanova
Keyword(s):  
Contact Problem ◽  
Equilibrium State ◽  
Equilibrium Problems ◽  
External Boundary ◽  
Fictitious Domain ◽  
Fictitious Domain Method ◽  
Rigidity Parameter ◽  
New Models ◽  
Crack Faces ◽  
Inequality Type

New models are investigated in this paper, that describe equilibrium states of plates with Signorini type nonpenetration conditions. In these models, it is assumed that under appropriate loading, plates have special deformations with already known configurations of edges. For this case, we deal with new non-penetration conditions that allow us to describe more precisely the possibility of contact interaction of plate edges. Using the method of fictitious domains, it is proved that an original contact problem for a plate can be obtained by passing to the limit when a rigidity parameter tends to infinity from a family of auxiliary problems formulated in a wider domain. The mentioned family of problems model an equilibrium state of plates with a crack and depend on the positive rigidity parameter. For these problems, to prevent a mutual penetration of the opposite crack faces boundary conditions of inequality type are imposed on the inner boundary corresponding to the crack. For the problem, describing a plate with a crack that intersects the external boundary at zero angle (a case of a boundary having one cusp), the unique solvability is proved.

scholarly journals On the existence of high-frequency boundary resonances in layered elastic media

2015 ◽  
Vol 471 (2178) ◽  
pp. 20140878 ◽  
Author(s):  
K. D. Cherednichenko ◽  
S. Cooper
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
High Frequency ◽  
Three Dimensional ◽  
Homogeneous Medium ◽  
Elastic Media ◽  
Displacement Boundary ◽  
Boundary Spectrum ◽  
New Type ◽  
High Frequency Vibrations

We analyse the asymptotic behaviour of high-frequency vibrations of a three-dimensional layered elastic medium occupying the domain Ω =(− a , a ) 3 , a >0. We show that in both cases of stress-free and zero-displacement boundary conditions on the boundary of Ω a version of the boundary spectrum, introduced in Allaire and Conca (1998 J. Math. Pures. Appl. 77, 153–208. ( doi:10.1016/S0021-7824(98)80068-8 )), is non-empty and part of it is located below the Bloch spectrum. For zero-displacement boundary conditions, this yields a new type of surface wave, which is absent in the case of a homogeneous medium.

scholarly journals Analysis of Multiple Fatigue Cracks—Part II: Results

1992 ◽  
Vol 114 (3) ◽  
pp. 462-468 ◽  
Author(s):  
M. C. Dubourg ◽  
M. Godet ◽  
B. Villechaise
Keyword(s):  
Load Transfer ◽  
Fatigue Cracks ◽  
Interfacial Crack ◽  
Frictional Resistance ◽  
Mode I ◽  
Crack Interaction ◽  
Intensity Factors ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Crack Faces

A semianalytical model of multiple fatigue crack analysis in sliding contact is developed. Linear elastic fracture mechanics is applied. Frictional resistance between crack faces is taken into account. Five crack interaction mechanisms have been identified. Load transfer between cracks can cause both significant increases and drops in stress intensity factors both in mode I and II. The interaction depends on the distance between cracks, their relative position with respect to the loading zone, and the interfacial crack coefficient of friction.

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