The stressed state of glass disks during strength testing

Kosarchin, V. I.; Margolin, A. M.; Osadchuk, V. A.; Chernukha, Yu. A.

doi:10.1007/bf01097870

J Math Sci

1993

DOI: 10.1007/bf01097870

|View full text |Cite

The stressed state of glass disks during strength testing

V. I. Kosarchin¹,

A. M. Margolin²,

V. A. Osadchuk³

et al.

Abstract: By applying the improved theory of plates, which makes it possible to determine all components of the stress tensor, we study the stressed state of glass disks under axisymmetric bending. We obtain a closedform solution of the corresponding boundary-value problem for systems of singularly perturbed equations. It is shown that the size of the zone of "pure" bending--the domain with uniformly stretched surface-differs from those known in the literature. The results obtained make it possible to determine the opti… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1996

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 1 publication

(2 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus for a revised analysis of the stress concentrations near the inclusion we regard part of the shell as a plate of radius r.. Earlier studies of plates with foreign inclusions have shown [3,7,1] that the perturbation zone (the region in which the stressed state differs significantly from that obtained by the standard theories of plates) has a width of the same order as the thickness of the plate. On that basis and on the basis of the results shown in Fig.…”

mentioning

confidence: 98%

See 1 more Smart Citation

Revised analysis of the thermal stresses in a shallow spherical shell with a foreign inclusion

Chernukha¹,

Kosarchin²

1996

J Math Sci

Self Cite

View full text Add to dashboard Cite

We carry out a revised analysis of the concentration of thermal stresses in a shallow spherical shell with a small foreign inclusion. We show that near the interface of the materials the stressed state has a sharply expressed three-dimensional character; thus the stresses differ significantly (both qualitatively and quantitatively) from the shells predicted by the standard thearies_.The study of thermal stresses in shells with a foreign inclusion is of great value in applications, in particular in connection with the manufacture, testing, and use of electrovacuum devices. A bibliography devoted to this problem can be found in the monograph of Podstrigach, Kolyano, and Semerak [2]. However, nearly all the results known in the literature on this problem were obtained by applying shell theories that do not provide a sufficiently complete description of the effects connected with the three-dimensional nature of the stressed state in the contact zones.At the same time the study of the thermally stressed state of plates with foreign inclusions carried out using the revised theory of plates [6] has shown [3,7] that in the contact zones the stressed state differs from that predicted by the standard theories of plates. These effects have a boundary-layer character and arise at a distance from the contact surface commensurate with the thickness of the plate. The presence of such effects caused by the foreign matter, should be observed also in thin-walled shell structures.In the present paper we conduct a revised analysis of the thermally stressed state in the contact zone of a shell as follows. From the theory of shells we determine the thermally stressed state of a shell containing a round inclusion. On the basis of a parametric analysis of this solution we identify a contact zone of the shell that can be replaced by an annular plate without any significant distortion of the contact stresses. Then, using the revised theory of plates, which makes it possible to determine all the components of the stress tensor [6], we determine the stressed state of a circular plate with a foreign inclusion; the boundary conditions for this problem are formulated by applying the solution obtained from shell theory.Consider a uniformly heated shallow spherical shell containing a small foreign inclusion of radius r0. The thickness of the shell and the inclusion are the same and equal to 2h. For the shallow spherical shell we take the initial data to be the following system of key equations [4]:Here ~ is the stress function, w is the deflection, T is the temperature, R is the radius of the shell, E is the Young's modulus, v is the Poisson coefficient, ~ is the temperature coefficient of linear expansion, and A is the Laplacian. We introduce the following notation for the Kelvin functions [5]:~2i_1(X) = f2i(X), ~2i(X)=--f2i_l(Z), i=l,2.Then the general solution of the system (1) can be represented as

show abstract

mentioning

confidence: 98%

“…2 we assume that r. = 5h. Moreover we recall that for a revised analysis it suffices to consider only the symmetric problem (relative to the middle surface) [1,3,7].…”

mentioning

confidence: 99%

Revised analysis of the thermal stresses in a shallow spherical shell with a foreign inclusion

Chernukha¹,

Kosarchin²

1996

J Math Sci

Self Cite

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

The stressed state of glass disks during strength testing

Cited by 1 publication

References 1 publication

Revised analysis of the thermal stresses in a shallow spherical shell with a foreign inclusion

Revised analysis of the thermal stresses in a shallow spherical shell with a foreign inclusion

Contact Info

Product

Resources

About