References
- Vekua , IN . 1965 . Theory of thin shallow shells of variable thickness . Akad. Nauk Gruzin. SSR Trudy Tbiliss. Mat. Inst. Razmadze , 30 : 3 – 103 . (Russian)
- Vekua , IN . 1955 . On a Way of Calculating of Prismatic Shells , Vol. 21 , Proceedings of A. Razmadze Institute of Mathematics of Georgian Academy of Sciences . pp. 191–259 (Russian)
- Vekua , IN . 1985 . Shell Theory: General Methods of Construction, Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics , Vol. 25 , Boston , , MA : Pitman (Advanced Publishing Program) .
- Jaiani , GV . 2011 . Cusped Shell-like Structures, SpringerBriefs in Applied Science and Technology , Heidelberg, Dordrecht, London, New York : Springer .
- Avalishvili , M and Gordeziani , D . 2003 . Investigation of two-dimensional models of elastic prismatic shell . Georgian Math. J. , 10 ( 1 ) : 17 – 36 .
- Gordeziani , DG . 1974 . On the solvability of some boundary value problems for a variant of the theory of thin shells . Dokl. Akad. Nauk SSSR , 215 ( 6 ) : 1289 – 1292 . (Russian)
- Gordeziani , DG . 1974 . To the exactness of one variant of the theory of thin shells . Dokl. Acad. Nauk SSSR , 216 ( 4 ) : 751 – 754 . (Russian)
- Gordeziani , D and Avalishvili , G . 2005 . On a dynamical hierarchical model for prismatic shells in the theory of elastic mixtures . Math. Methods Appl. Sci. , 28 : 737 – 756 .
- Gordeziani , D , Avalishvili , M and Avalishvili , G . 2005 . Dynamical hierarchical models for elastic shells . Appl. Math. Inform. Mech. , 10 ( 1 ) : 19 – 38 .
- Dauge , M , Faou , E and Yosibash , Z . 2004 . “ Plates and shells: Asymptotic expansions and hierarchical models ” . In Encyclopedia of Computational Mechanics , Edited by: Erwin , Stein , de Borst , René and Hughes , Thomas JR . 199 – 236 . Chichester : John Wiley & Sons, Ltd .
- Vogelius , M and Babuška , I . 1981 . On a dimensional reduction method. I. The optimal selection of basis functions . Math. Comp. , 37 ( 155 ) : 31 – 46 .
- Vogelius , M and Babuška , I . 1981 . On a dimensional reduction method. II. Some approximation-theoretic results . Math. Comp. , 37 ( 155 ) : 47 – 68 .
- Jaiani , GV , Kharibegashvili , SS , Natroshvili , DG and Wendland , WL . 2003 . Hierarchical Models for Elastic Cusped Plates and Beams, Lecture Notes of TICMI , Vol. 4 , Tbilisi : Tbilisi University Press . (For electronic version see: http://www.emis.de/journals/TICMI)
- Jaiani , GV , Kharibegashvili , SS , Natroshvili , DG and Wendland , WL . 2004 . Two-dimensional hierarchical models for prismatic shells with thickness vanishing at the boundary . J. Elasticity , 77 ( 2 ) : 95 – 122 .
- Jaiani , GV . 1988 . The First Boundary Value Problem of Cusped Prismatic Shell Theory in Zero Approximation of Vekua's Theory , Vol. 29 , Proceedings of I. Vekua Institute of Applied Mathematics of Tbilisi University . pp. 5–38 (Russian)
- Jaiani , G . 1982 . Solution of some Problems for a Degenerate Elliptic Equation of Higher Order and their Applications to Prismatic Shells , Tbilisi : Tbilisi University Press . (in Russian with Georgian and English summaries)
- Krasnov , SN . 1959 . Mixed boundary value problems for degenerate linear hyperbolic differential equations of the second order . Mat. Sb. , 49 ( 91 ) : 29 – 84 . (Russian)
- Baranovskii , FT . 1960 . A mixed problem for a degenerate hyperbolic equation . Izv. Vyssh. Uch. Zaved., Mat. , 3 ( 16 ) : 30 – 42 . (Russian)
- Briukhanov , VA . 1972 . On a mixed problem for a hyperbolic equation degenerating on a part of the domain boundary . Differ. Uravneniya , 8 ( 1 ) : 3 – 6 . (Russian)
- Vragov , VN . 1972 . A mixed problem for a class of hyperbolic-parabolic equations of the second order . Differ. Uravneniya , 12 ( 1 ) : 24 – 31 . (Russian)
- Vragov , VN . 1983 . Boundary Value Problems for Nonclassical Equations of Mathematical Physics , Novosibirsk : Novosibirsk University Press . (Russian)
- Chinchaladze , N , Gilbert , R , Jaiani , G , Kharibegashvili , S and Natroshvili , D . 2010 . Cusped elastic beams under the action of stress and concentrated forces . Appl. Anal. , 89 ( 5 ) : 757 – 774 .
- Jaiani , GV and Kharibegashvili , SS . 2001 . Dynamical problems in the (0,0) and (1,0) approximations of a mathematical model of cusped bars , their interactions, and applications to partial differential equations, Graz, Austria, 12–16 February : Proceedings of the International Graz Workshop on Functional-analytic and complex methods . pp. 188–247
- Chinchaladze , N . 2007 . Vibration of an Elastic Plate under the Action of an Incompressible Fluid , Proceedings of the IUTAM Symposium on the Relations of Shell. IUTAM Bookseries, Vol. 9 . Plate, Beam, and 3D Models Dedicated to the Centenary of Ilia Vekua's Birth, Tbilisi, GA, 23–27 April, Springer, 2008, pp. 77–90
- Chinchaladze , N and Gilbert , R . 2006 . Vibration of an elastic plate under action of an incompressible fluid in case of N=0 approximation of I. Vekuas hierarchical models . Appl. Anal. , 85 ( 9 ) : 1177 – 1187 .
- Chinchaladze , N and Gilbert , R . 2005 . Cylindrical vibration of an elastic cusped plate under action of an incompressible fluid in case of N=0 approximation of I. Vekuas hierarchical models . Complex Var. , 50 ( 7–11 ) : 479 – 496 .
- Chinchaladze , N . 2002 . Vibration of the Plate with Two Cusped Edges , Vol. 52 , Proceedings of I.Vekua Institute of Applied Mathematics of Tbilisi State University . pp. 30–48
- Jaiani , G . 1999 . Oscillation of an Orthotropic Cusped Plate , Vol. 14(1) , Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics of Tbilisi State University . pp. 24–31
- Vishik , MI . 1954 . Boundary value problems for elliptic equations degenerating on the domain boundary . Mat. Zb. , 35 ( 77:3 ) : 513 – 568 . (Russian)
- Ladizhenskaya , OA . 1963 . The Mathematical Theory of Viscous Incompressible Flow , New York : Gordon & Breach .
- Chinchaladze , N , Gilbert , R , Jaiani , G , Kharibegashvili , S and Natroshvili , D . 2008 . Existence and uniqueness theorems for cusped prismatic shells in the N-th hierarchical model . Math. Methods Appl. Sci. , 31 ( 11 ) : 1345 – 1367 .
- Devdariani , G , Jaiani , G , Kharibegashvili , S and Natroshvili , D . 2000 . Some mathematical problems related to the first approximation of I. Vekua's theory for cusped prismatic shells . Appl. Math. Inform. , 5 ( 2 ) : 26 – 46 .
- Evans , LC . 1998 . Partial Differential Equations, Grad. Stud. Math. , Vol. 19 , Providence , , RI : American Mathematical Society .
- Mikhlin , SG . 1968 . Mathematical Physics , Moscow : Nauka . (Russian)
- Fikhtengolz , GM . 1969 . Differential and Integral Calculus , Vol. I , Moscow : Nauka . (Russian)