ON DEFLECTIONS OF A PRISMATIC SHELL EXPONENTIALLY CUSPED AT INFINITY IN THE N = 0 APPROXIMATION OF HIERARCHICAL MODELS

Article Sidebar

PDF
Published: Mar 12, 2017
Keywords:
Cusped Prismatic Shells, Cusped Plates, Vekuas’s Hierarchical Models, Degenerate Partial Differential Equations, Elliptic Equations, Reimann Function

Main Article Content

Miranda Gabelaia

Abstract

In the N = 0 approximation of hierarchical models the well-posedness of boundary value problems for an equation of deflections of a prismatic shell exponentially cusped at infinity is studied. Static problem of the shell with the thickness as follows ( ) 0 2 2 2 1 x x h h e     , h0  const  0,   const  0, x1 (,), x2  0 , is given and investigated. The solution of the posed boundary value problem is given in an integral form.

Article Details

Issue
Vol. 389 No. 1 (2016)
Section
Materials Physics

References

Vekua I. (1955). On one method of calculating of prismatic shells. Trudy Tbilis.

Mat. Inst. 21, 191–259 (in Rus.)

Vekua I. (1985). Shell Theory: General Methods of Construction. Boston: Pitman

Advanced Publishing Program

Jaiani G. (2011). Cusped Shell-like Structures. Heidelberg-Dorbrecht-London-New

York: Springer

Avalishvili M., Gordeziani D. (2001). Investigation of a hierarchical model of

prismatic shells. Bull. Georgian Acad. Sci., 165(3), 485-488.

Chinchaladze N., Gilbert R.P., Jaiani G., Kharibegashvili S., Natroshvili D.

(2008). Existence and uniqueness theorems for cusped prismatic shells in the N-th hierarchical

model. Mathematical Methods in Applied Sciences, 31, 11, 1345-1367, DOI 10.1002

/mma.975, for the electronic version see: http://www3.interscience.wiley.com/

Jaiani G. (2001). Application of Vekua’s dimension reduction method to cusped

plates and bars. Bull. TICMI, 5, 27-34.

Jaiani G., Kharibegashvili S., Natroshvili D., Wendland W. (2004). Twodimensional

hierarchical models for prismatic shells with thickness vanishing at the boundary.

Journal of Elasticity, 77 (2), 95-122.

Jaiani G., Kharibegashvili S., Natroshvili D., Wendland W.L. (2003). Hierarchical

Models for Elastic Cusped Plates and Beams. Lecture Notes of TICMI, 4.

Meunargia T. (1999). On one method of construction of geometrically and

physically nonlinear theory of non-shallow shells. Proceedings of A.Razmadze Mathematical

Institute, Georgian Academy of Sciences, 119, 133-154.

Mikhlin S.G. (1970). Variational Methods in Mathematical Physics. Moscow:

Nauka (in Rus.)

Bitsadze A. (1981). Some Classes of Partial Differential Equations. Moscow:

Nauka (in Rus.)

Vekua I. (1948). New Methods of Solution of Elliptic Equations. MoscowLeningrad:

Gostekhizdat (in Rus.)