scholarly journals Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

Technologies ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 59
Author(s):  
Evgeny Rudoy
Keyword(s):  
Small Parameter ◽  
Equilibrium Problem ◽  
Elastic Properties ◽  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Asymptotic Model ◽  
Hard Inclusion ◽  
Passage To The Limit

An equilibrium problem of the Kirchhoff–Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing the width of the inclusion ε as εN with N<1. The passage to the limit as the parameter ε tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion (N<−1) and elastic inclusion (N=−1). The inhomogeneity disappears in the case of N∈(−1,1).

scholarly journals Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions

2020 ◽  
Author(s):  
Evgeny Rudoy
Keyword(s):  
Small Parameter ◽  
Equilibrium Problem ◽  
Elastic Properties ◽  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Asymptotic Model ◽  
Hard Inclusion ◽  
Passage To The Limit

An equilibrium problem of the Kirchhoff-Love plate containing a nonhomogeneous inclusion is considered. It is assumed that elastic properties of the inclusion depend on a small parameter characterizing width of the inclusion $\varepsilon$ as $\varepsilon^N$ with $N&lt;1$. The passage to the limit as the parameter $\varepsilon$ tends to zero is justified, and an asymptotic model of a plate containing a thin inhomogeneous hard inclusion is constructed. It is shown that there exists two types of thin inclusions: rigid inclusion ($N&lt;-1$) and elastic inclusion ($N=-1$). The inhomogeneity disappears in the case of $N\in (-1,1)$.

The Influence of the Shape and Rigidity of an Elastic Inclusion on the Transverse Flexure of Thin Plates

1943 ◽  
Vol 10 (2) ◽  
pp. A69-A75
Author(s):  
Martin Goland
Keyword(s):  
Stress Distribution ◽  
Future Study ◽  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Thin Plates ◽  
Elastic Plates ◽  
Perforated Plates ◽  
Circular Rigid Inclusion ◽  
Special Cases ◽  
Elastic Inclusions

Abstract The purpose of this paper is to investigate the influence of several types of inclusions on the stress distribution in elastic plates under transverse flexure. An “inclusion” is defined as a close-fitting plate of some second material cemented into a hole cut in the interior of the elastic plate. Depending upon the properties of the material of which it is composed, the inclusion is described as rigid or elastic. In particular, the solutions presented will deal with the effects of circular inclusions of differing degrees of elasticity and rigid inclusions of varying elliptical form. Since the rigid inclusion and the hole are limiting types of elastic inclusions, and the circular shape is a special form of the ellipse, plates with either a circular hole or a circular rigid inclusion are important special cases of this discussion. It is hoped that the present analysis of several types of inclusions will aid in a future study of perforated plates stiffened by means of reinforcing rings fitted into the holes.

An elastic harmonic inclusion near a rigid harmonic inclusion loaded by a couple

2019 ◽  
Vol 84 (3) ◽  
pp. 555-566
Author(s):  
Xu Wang ◽  
Liang Chen ◽  
Peter Schiavone
Keyword(s):  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Complex Loading ◽  
Solution Procedure ◽  
External Loading ◽  
Surrounding Matrix ◽  
The Matrix ◽  
Mapping Techniques ◽  
Loading Parameter ◽  
Harmonic Inclusion

AbstractWe use conformal mapping techniques to solve the inverse problem concerned with an elastic non-elliptical harmonic inclusion in the vicinity of a rigid non-elliptical harmonic inclusion loaded by a couple when the surrounding matrix is subjected to remote uniform stresses. Both a size-independent complex loading parameter and a size-dependent real loading parameter are introduced as part of the solution procedure. The stress field inside the elastic inclusion is uniform and hydrostatic; the interfacial normal and tangential stresses as well as the hoop stress on the matrix side are uniform along each one of the two inclusion–matrix interfaces. The tangential stress along the interface of the elastic inclusion (free of external loading) vanishes, whereas that along the interface of the rigid inclusion (loaded by the couple) does not. A novel method is proposed to determine the area of the rigid inclusion.

METHOD OF ASYMPTOTIC PARTIAL DECOMPOSITION OF DOMAIN

1998 ◽  
Vol 08 (01) ◽  
pp. 139-156 ◽  
Author(s):  
G. P. PANASENKO
Keyword(s):  
Small Parameter ◽  
Interface Conditions ◽  
Singular Behavior ◽  
Common Boundary ◽  
Partial Decomposition ◽  
Regular Behavior ◽  
Different Dimensions ◽  
The Common ◽  
Different Parts ◽  
Passage To The Limit

A new method of partial decomposition of a domain is proposed for partial differential equations, depending on a small parameter. It is based on the information about the structure of the asymptotic solution in different parts of the domain. The principal idea of the method is to extract the subdomain of singular behavior of the solution and to simplify the problem in the subdomain of regular behavior of the solution. The special interface conditions are imposed on the common boundary of these partially decomposed subdomains. If, for example, the domain depends on the small parameter and some parts of the domain change their dimension after the passage to the limit, then the proposed method reduces the initial problem to the system of equations posed in the domains of different dimensions with the special interface conditions.

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