T.Vashakmadze Home Page

TAMAZ VASHAKMADZE

Official adress	I. Vekua Institute of Applied Mathematics of Tbilisi State University 2,University St.380043, Tbilisi, 43, Georgia Tel.: (+99532) 30 30 40 (of.); (+99532) 23 09 18 (h.) E-mail: Vasha@viam.hepi.edu.ge
Marital status	Married, two children
Nationality	Georgian
Date of birth	Born on September 16, 1937, in Tbilisi, Republic of Georgia

Education	1959	graduated from Tbilisi St. University for Mechanics and Mathematics,
	1962	Postgraduated from Razmadze Inst. of Math. Academy of Sci. of Georgia (Razmadze Inst.)
Academic Degree	1964	Ph. D. (Candidate of Sci.) in Computational Mathematics Razmadze Inst. Theses: Numerical Solution of Some Boundary Value Problem for Ordinary differential equation;
	1984, 1987	Dr.Hab. (Full professor) in Mechanics of Solids. Preliminary: Lomonosov Moscow St. University Dep-t of Mechanics of Solids (1984). Officially: Razmadze Inst (1987). Theses: Solution of Basic Problems of Elasticity Theory for Cylyndrical Regions (Opponents: acad. S.Ambartsumian, acad. I.Vorovich, acad. S.Mikhlin, prof. V.Kondratiev)
Recent employmen	1973-Present.	Professor of mathematics, Tbilisi State University, September,1988-Present. Head of Dept. Vekua Institute of Applied Mathematics,February,
Editorships	Member of Editorial Boards of Vekua Institute of Applied Mathematics, Main editor of journal "Proceedings of Javakhishvili Tbilisi State University, Applied Mathematics and Computer Sciences"
Prizes and Awards	1999	Grant of the National Academy of Scienses (NAS) and U.S. Recipient of Colaboration in Basic Scienses and Engineering (COBASE) (with Collaborators of Department of Matematical Scienses of University of Delawere)
	1997	Medal of Ivane Javakhishvili
	1995	Long-term Research Grant of ISF (Fund of G.Soros),
	1993	Short-term Research Grant of ISF
	1993	Vekua's Prize of Georgian Academy of Sciences
	1959	First-Prize of Diploma-work of Tbilisi State University
Field of Research	Solid Mechanics, Numerical Analysis, Computer Sci.
Any international work experience	Member of Inter. Societies of InterAction Math. & Mech. (1979), of IS of BEM (1992), Georgian Math. Union (1964) Vice-president of Georgian Society of "Theoretical and Applied Mechanics", Vice-president of Georgian Society "History of Siences", Member of organized commitees 12 AllUnion of FSU and International conferences.
Main lecture cources	Mathematical analyses and analytical geometry The DE of Mathematical Physics Numerical Methods The mathematical theory of elastic plates and shells The theory and applications of orthogonal functions Projective Methods The technology of solutions of systems of linear alqebraic eqvations with rare matrices Introduction in one and two-dimansional spline-function theory The mathematical modeling of some problems of solid mechanics
Scientific Intersts	My research to date has mainly focused on models of elastic shells and plates, in particular, I have used averaging methods and asymptotic methods to model anisotropic plates and shells of variable thickness. By projective methods allow one to reduce the three-dimensional elastic theory to an approximate two-dimensional elastic theory. In this respect methods of reduction, known in the literature usually being based on simplifying hypotheses, are studied. In contradiction to classical methods the problems, connected with construction of refined theories of anisotropic nonhomogeneous plates with variable thickness without assumption of any physical and geometrical restrictions, are investigated. The comparative analysis of such reduction methods was carried out and the following fact was established: the error transition, occurring with substitution of two-dimensional model for the initial problem on the class of assumed solutions is restricted from below. In addition, I have modeled dynamical piezoelectric and electric conducting elastic plates, corresponding to nonlinear cases. Further, Vekua`s method of reduction, containing regular process of study of three-dimensional problem, is investigated. In this direction, the problems, connected with solvability, convergence of processes and construction of effective algorithms of approximate solutions are studied. We also consider methods of approximate solution of two-dimentional boundary value problems for the system of differential equations, which arose also as necessary step for solving two-dimensional dynamical models corresponding to boundary value problems for elastic plates and shells. My research would have points of contact with Prof.R.Gilbert's work on elasto-plastic, and poro-elastic plates. In particular, I would be interested in working on models of the seabed that could be compared to the poro-elastic plate. In particular my model of plates with variable thickness might lead to a more realistic description of the seabed, which is in general not uniform in thickness. The formulating of the scattering problem of elastic or thermo-elastic obstacles in a heterogeneous elastic, anisotropic medium is both intriguing and challenging.
Languages	Georgian, Russian, English, German
Publications	Number of papers: 95 articles, 4 monographs 1.To justification of von Karman-Reissner type equations and mathematical modeling of poroelastic media. Comp. Fluid Dynamics, CFD/CFD journal, 2001,pp.95-104(Report on Russian-Japan 7-th RJ7CFD July, 2000). 2. A two-dimensional nonlinear theory of anisotropic plates, Mathematical and Computer Modeling,v.32,issue 7-8,2000,pp.855-875.(co-author R. Gilbert). 3. To justification of von Karman equations and math. model. poroelastimedia, Izvestia vuzov. Severo-Kavkazskii region,Estetstvennie nauki,tom 3, 2000 (with R.Gilbert, in Russian). 4. The Theory of Anisotropic Elastic Plates,Kluwer Academic Publishers, Dortrecht/Bosto/London, xvi+240 pp.ISBN 0-7923-5695-0.,1999.(in Math.Review:2001a:74065). 5. Some problems of computational mechanics of rigid deformed body, Facta Univ. Ser. Mech. Automat. Control Robot.2, No 6, 1996, pp.39-56.(99e:73067). 6. Mathematical modelling of some problems for elastic plates, Geometric function theory and applications of complex analysis to mechanics: Complex analysis.appl.to PDE,2,(Halle,1988),176-185,Pitman Res. Notes Math.Ser., 257, Longman Sci. Tech., Harlow, 1991(92k:73k10). 7. The theory of elastic plates, Advances in Mech.11, No 3, 1988, pp.43-76 (90g:73081,in Russian). 8. On Vekua's theory of elastic plates and shells, Current problems in mathematical physics, v. II, Tbilis. Gos. Univ. Tbilisi, 1987, pp. 200-207, 1987 (90b:73036,in Russian). 9. On the theory of Vekua for elastic plates. Sem. Inst. Prikl. Mat. Dokl. No 20, pp.15-22,1986 (89a:73042,in Russian). 10. Nekotorie voprosy matematicheskoi teorii anisotropnikh uprugikh plastin. Some problems of the mathematical theory of anisotropic elastic, Tbilis. Gos. Univ., Tbilisi,176pp., 1986, (88g:73016, in Russian). 11. On the theory of plates. Sem. Inst. Prikl. Mat. Dokl., No 18, 1984, pp.6-17 (87e:73079,in Russian). 12. On the constuction of refined theories of anisotropic plates. Sem. iInst. Prikl. Mat. Dokl., No 17, pp. 18-24,1983 (85a:73056, in Russian). 13. On the application of orthogonal polynomials in the theory of elasticity. Sixth International Conference on Numerical Methods in Fluid Dynamics, Proc. Conf., Tbilisi, 1978, pp. 537-541, Lecture Notes in Phys., 90, Springer, Berlin/New-York, 1979(84d:73016). 14. On the accuracy of approximation of a problem of elasticity theory. Soviet Mathem. Dokl., v.24, No 3, pp.568-570, 1981(83e:73019). 15. Error estimation of the transition from some three-dim.problems of elasticity theory to some two-dim. models. Sem. Inst. Prikl. Mat. No 15, pp. 57-66, 1981,(83g:73054,in Russian). 16. On applications of a variational-difference method to thesolution of some shell theory problems. Theory of Shells (Proc.Third IUTAM Sympos., Tbilisi, 1978), pp.575-581, North-Holland, Amsterdam/New-York,1980 (81h:73L99). 17. An investigation of Vekua'soperator of the theory of elastic shells. Complex analysis and its applications, "Nauka", Moscow, pp. 102-107, 1978 (80c:73060). 18. Some mathem.problems of the theory of nonlinear elasticity. Trends in appl. of mathem. to mechanics (Lisbon,1994), pp. 348-357, Pitman Monogr. Serveys Pure&appl. Math., 77, Longman, Harlow, 1995,(CMP1 475 498, 98:02,73C50). 19. On the problem of constucting the mathem.theory of plates and shells.Trends Appl. Mathem. to Mech. (Wassenaar,1987), 273 79, Springer, Berlin,1988, (CMP 976 898). 20. On the Korn type inequality and problem of justification of refined theories for elastic plates.Trends Appl.Mathem.to Mech.(Bad-Honnef,1985,pp.487-491,Lecture Notes in Phys., Springer, Berlin,1986(CMP 851 819). 21. Package of Applied Programs of Design of Spatial Structures (Mathematical modeling,Algorithms and Software),Javakhishvili Tbilisi St. Univ. v. I-162pp. v. II-166pp., 1982. 22. Variational formulation for refined theories, generalized Hellinger-Reissner variational principle (extract from lectures). Bulletin of TICMI (Tbilisi International Centre in Mathematics and Informatics), vol 2, pp.13-17, 1998. 23. On the contraction of a mathematical theory of anisotropic nonhomogeneous elastic plates and shells. Advance Course of Theory of Elasticity 2(The manuscript of five lectures [60pp.] for participants of TICMI from 09/17/1998 till 09/221998 ), Bulletin of TICMI, vol.2, 1998. 24. On the analysis of numerical methods solving BVP for second order ODE-s with a small parameter. Applied Mathematics and Informatics, v.I, pp.83-97, 1997 (co-author A.Muradova) 25. To design shearing forces for elastic plates, Bulletin TICMI, vol.1, p.17, 1997 (co-author A.Muradova) 26. Some mathem. problems of the plate theory, Modern Problems of Continuum Mechanics (Anniversary of acad. Vorovich), Rostov/Don, pp. 47-54,1995 (in Russian). 27. Some mathematical problems of magneto-pieso-elasticity, electro-magnetic forces and applications, Supplements, The International Journal of Appl. Electromagnetic in Materials, Elsevier, v.2, pp.411-414. 1992 (Conference in Sendai, Japan, 1991). 28. On the Mathematical theory of piezoelectric and electric conductive elastic plates, Trends Appl.Math. to Mech., Longman Sci.& Tech., 1991, 236-241. 29. Mathematical modeling of some problems for elastic plates,Pitman Research Notes, 257, Longman Sci. & Tech., pp. 176-185,1991. 32. Generalized factorization method and its application for approximate solution of some problems of mathematical physics, Proc. Sym. Continuum Mechanics and Related Problems of Analysis (Anniversary of Acad. Muskhelishvili), Metsniereba, Tbilisi, v.1, pp.36-45, 1971. 33. A generalized finite-difference method, Differentsial'nie Uravnenia, v.II, No 5, pp.614-618, 1966. 34. To numerical solution of boundary value problems, Jurnal Vichislitelnoi Matematiki i matematicheskoi Fiziki, Vol.4, No.4, 1964, 623-637 (in Russian).

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