VIAM

Natalia Chinchaladze

Directorate / Elasticity and Shell Theory Department
Deputy Director / Senior Researcher
Office: room 118, University str.11, 0186 Tbilisi, Georgia
Phone: +995591938233
E-mail: chinchaladze@gmail.com
Research fields: Partial Differential Equations. Mathematical Modeling. Shell and Plate Theory, Cusped Plates and Shells. Solid-fluid Interaction Problems

Summary

EDUCATION
2003: Ph.D. (Candidate of Sci.) in Mechanics of Deformable Bodies, Iv. Javakhishvili Tbilisi State University. Thesis: "On Elastic Cusped Plate – Viscous Fluid Interaction Problems" (Advisor: Professor George Jaiani);
1997-2000: Post-graduate student of Tbilisi State University;
1.09-20.12.1999: Visitor Post-graduate Student of Danish Centre of Applied Mathematics and Informatics (Faculty of Fluid Dynamics, Technical University of Denmark, Lyngby, Denmark)

Work Experience:
30.03.2016-up to now I. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences, Associated Professor
01.05.2012-28.02.2018 I. Javakhishvili Tbilisi State University, I. Vekua Institute of Applied Mathematics, Vice Director
10.03.2010-30.03.2016 I. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences, Assistant Professor
20.08.2007-16.03.2010 I. Javakhishvili Tbilisi State University, Faculty of Exact and Natural Sciences, Head of Laboratory
01.01.2007-20.08.2007 I. Javakhishvili Tbilisi State University, I. Vekua Institute of Applied Mathematics, Researcher
01.12.2003-01.12.2006 I. Javakhishvili Tbilisi State University, I. Vekua Institute of Applied Mathematics, Senior Researcher
01.01.1997-01.12.2003 I. Javakhishvili Tbilisi State University, I. Vekua Institute of Applied Mathematics, Junior Researcher
02.09.1996-01.01.1997 I. Javakhishvili Tbilisi State University, I. Vekua Institute of Applied Mathematics, Engineering

OTHER ACTIVITIES
January 2012-present: Vice Chair of the Georgian Mechanical Union
March 2006-2013: Scientific Secretary of GMU (Georgian Mathematical Union)
2005-present: Member of ISAAC (International Society for Analysis, its Applications and Computation) http://www.math-isaac.org
2005-present: Member of the Georgian National Committee of the Theoretical and Applied Mechanics
2002- present: Managing Editor of Bulletin of TICMI (http://www.emis.de/journals/TICMI)
2002- present: Managing Editor of Lecture Notes of TICMI (http://www.emis.de/journals/TICMI)
2001- present: Member of GMU
20-29.08.2001:Participate in the Summer School "Simulation of Fluid and Structure Interaction", Prague, Czech Republic
2000- present: Member of Tbilisi International Centre of Mathematics and Informatics

Projects

Talks

Zero Approximation of Hierarchical Models for Fluids in Pipes of Angular Cross-Sections, by Natalia Chinchaladze (Speaker) at The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS", Tbilisi, Georgia, 13-15 September, 2023.
I. Vekua Institute of Applied Mathematics of TSU - 55, by Natalia Chinchaladze (Speaker), George Jaiani at XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia, 29-31 August, 2023.
A DYNAMICAL PROBLEM OF ZERO APPROXIMATION OF HIERARCHICAL MODELS FOR FLUIDS, by Natalia Chinchaladze (Speaker) at XIV Annual International Meeting of the Georgian Mechanical Union, Poti, Georgia, 28-31 August, 2023.
MOTION OF VISCOUS FLUID IN PRISMATIC SHELL-LIKE DOMAINS IN CASE OF ZEROTH APPROXIMATION OF HIERARCHICAL MODELS, by Natalia Chinchaladze (Speaker) at XIII Annual International Meeting of the Georgian Mechanical Union, Batumi, Georgia, 24-26 August, 2022.
On a problem in N=0 approximation of hierarchical models of incompressible fluid, by Natalia Chinchaladze (Speaker) at XXXVI International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University , Tbilisi, Georgia, 19-21 April, 2022.
ON A PROBLEM OF NON-HOMOGENEOUS PIEZOELECTRIC ELASTIC ROD WITH VARIABLE CONSTITUTIVE COEFFICIENTS, by Natalia Chinchaladze (Speaker), Archil Sakevarashvili at XII Annual International Meeting of the Georgian Mechanical Union, Kutaisi, Georgia, 09-11 September, 2021.
On One Tension-compression Oscillation Problem of Hierarchical Model for Kelvin-Voigt Plates with Variable Thickness, by Natalia Chinchaladze (Speaker) at 13th ISAAC Congress, Ghent, Belgium, 02-06 August, 2021.
TICMI – 25 , by George Jaiani (Speaker), Natalia Chinchaladze at The Fifth International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering, Tbilisi, Georgia, 16-18 June, 2021.
Some comments concerning hierarchical models, by George Jaiani (Speaker), Natalia Chinchaladze at XXXV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia, 21-24 April, 2021.
On some tension-compression dynamical problems in the zero approximation of hierarchical models for Kelvin-Voigt plates with variable thickness, by Natalia Chinchaladze (Speaker) at XXXIV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia, 16-19 September, 2020.
ON SOME BOUNDARY PROBLEMS OF PIEZOELECTRIC TRANSVERSELY ISOTROPIC CUSPED BARS, by Natalia Chinchaladze (Speaker) at The Eight Annual Conference in Exact and Natural Sciences, Tbilisi, Georgia, 03-07 February, 2020.
On a dynamical problem of the transversely isotropic solids, by Natalia Chinchaladze (Speaker) at X Annual International Meeting of the Georgian Mechanical Union, Telavi, Georgia, 27-28 September, 2019.
Existence and Uniqueness Theorem for Cusped Kelvin-Voigt Elastic Plates in the Zero Approximation of the Hierarchical Models, by Natalia Chinchaladze (Speaker) at 12th International ISAAC Congress, Aveiro, Portugal, from 28 July to 03 August, 2019.
On application of I. Vekua’s dimension reduction method to hierarchical models of elastic shells , by Natalia Chinchaladze (Speaker), George Jaiani at The Ninth Congress of Romanian Mathematicians, Galati, Romania, from 28 June to 03 July, 2019.
On the variation formulation of BVPs for piezoelectric transversely isotropic cusped bars, by Natalia Chinchaladze (Speaker) at XXXIII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Tbilisi, Georgia, 23-25 April, 2019.
On a Vibration Problem of the Transversely Isotropic Solids, by Natalia Chinchaladze (Speaker) at The Seventh Annual Conference in Exact and Natural Sciences, Tbilisi, Georgia, 11-15 February, 2019.
ON A VIBRATION PROBLEM FOR POROUS ELASTIC CUSPED PRISMATIC SHELLS, by Natalia Chinchaladze (Speaker) at IX Annual International Meeting of the Georgian Mechanical Union, Kutaisi, Georgia, 12-14 October, 2018.
Existence and Uniqueness Theorems for Cusped Porous Elastic Prismatic Shells in the Zero Approximation of the Hierarchical Models, by Natalia Chinchaladze (Speaker) at 41st SOLID MECHANICS CONFERENCE, Warsaw, Poland, 27-31 August, 2018.
On a vibration problem of porous elastic prismatic shells, by Natalia Chinchaladze (Speaker) at XXXII Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Tbilisi, Georgia, 18-20 April, 2018.
On a Problem for Viscoelastic Kelvin-Voigt Prismatic Shells, by Natalia Chinchaladze (Speaker) at The Sixth Annual Conference in Exact and Natural Sciences, Tbilisi, Georgia, 12-15 February, 2018.
Cusped Prismatic Shell-Fluid Interaction Problems, by Natalia Chinchaladze (Speaker), Robert Gilbert at VIII International Conference of the Georgian Mechanical Union, Tbilisi, Georgia, 27-29 September, 2017.
Antiplane Strain (Shear) of Non-Homogeneous Prismatic Shell-Like Bodies, by Natalia Chinchaladze (Speaker) at GAMM 2017, Weimar, Germany, 06-10 March, 2017.
Antiplane Shear of Orthotropic Non-Homogeneous Prismatic Shells, by Natalia Chinchaladze (Speaker) at VII INTERNATIONAL JOINT CONFERENCE OF THE GEORGIAN MATHEMATICAL UNION & THE GEORGIAN MECHANICAL UNION, Batumi, Georgia, 05-09 September, 2016.
ANTIPLANE STRAIN (SHEAR) OF ORTHOTROPIC PRISMATIC SHELL-LIKE BODIES, by Natalia Chinchaladze (Speaker), George Jaiani at SolMech40, Warsaw, Poland, from 19 August to 02 September, 2016.
VEKUA’S DIMENSION REDUCTION METHOD FOR THE THIRD MODEL OF PRISMATIC SHELLS, by Natalia Chinchaladze (Speaker) at The Fourth Annual Conference in Exact and Natural Sciences, Tbilisi, Georgia, 26-28 January, 2016.
On some problems of biofilms occupying thin prismatic domains, by Natalia Chinchaladze (Speaker) at VI Annual meeting of the Georgian Mechanical Union, Tbilisi, Georgia, from 30 September to 04 October, 2015.
On a mathematical problem of cusped double-layered plates , by Natalia Chinchaladze (Speaker) at 86th Annual Meeting of the International Association of Applied Mathematics and Mechanics, Lecce, Italy, 23-27 March, 2015.
On a problem of cusped double-layered prismatic shells , by Natalia Chinchaladze (Speaker) at The Third Annual Conference in Exact and Natural Sciences, Tbilisi, Georgia, 02-07 February, 2015.
On some methods for calculating cusped prismatic shells , by Natalia Chinchaladze (Speaker) at V Annual meeting of the Georgian Mechanical Union, Tbilisi, Georgia, 08-10 October, 2014.
On a Variational Problem for a Cusped Elastic Prismatic Shells in Case of the Third Model of Vekua’s Hierarchical Model, by Natalia Chinchaladze (Speaker) at 39th SOLID MECHANICS CONFERENCE, Zakopane, Poland, 01-05 September, 2014.
On a Mathematical Model of a Cusped Double-Layered Prismatic Shell, by Natalia Chinchaladze (Speaker) at The 10th AIMS Conference on Dynamical Systems Differential Equations and Applications, Madrid, Spain, 07-11 July, 2014.
A boundary-transmission problem for two rectangularly linked elastic bars, by Natalia Chinchaladze (Speaker), George Jaiani at 28th Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Tbilisi, Georgia, 22-24 April, 2014.
On Some Analytic Methods for Calculating of Cusped Prismatic Shells and Beams, by Natalia Chinchaladze (Speaker) at 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics, Erlangen, Germany, 10-14 March, 2014.
On a Problem of Vibration of the Biofilm, by Natalia Chinchaladze (Speaker) at The Second Annual Conference in Exact and Natural Sciences, Tbilisi, Georgia, from 29 January to 03 February, 2014.
Some numerical methods for laminated prismatic shells in the zeroth approximations, by Natalia Chinchaladze (Speaker) at IV Annual Meeting of the Georgian Mechanical Union, Kutaisi, Georgia, 08-10 November, 2013.
Hierarchical models for biofilms occupying thin prismatic domains with a variable thickness , by Natalia Chinchaladze (Speaker) at SECOND INTERNATIONAL CONFERENCE ON "MODERN PROBLEMS IN APPLIED MATHEMATICS", Tbilisi, Georgia, 04-07 September, 2013.
On some analytical methods for calculating cusped prismatic shells , by Natalia Chinchaladze (Speaker) at The 9th ISAAC Congress, Krakow, Poland, 05-09 August, 2013.
Harmonic vibration of a cusped plate in the zero approximation of Vekua's hierarchical models , by Natalia Chinchaladze (Speaker) at 38th Solid Mechanics Conference, Warsaw, Poland, 27-31 August, 2012.
On a vibration of a cusped plane in the zero approximation of Vekua's hierarchical models, by Natalia Chinchaladze (Speaker) at Conference of Applied Analysis and Mathematical Biology, Newark, USA, 08-09 August, 2012.
Direct and inverse elastic beams-fluid interaction problems, by Natalia Chinchaladze (Speaker) at Sixth International Conference "Inverse Problems: Modeling and Simulation", Antalya, Turkey, 21-26 May, 2012.
Cubature of the Solution of the Dirichlet Problem for Euler–Poisson–Darboux Equation in the Half-plane by Approximate Quasi-Interpolation, by Natalia Chinchaladze (Speaker) at II International Conference of the Georgian Mathematical Union, Batumi, Georgia, 15-19 September, 2011.
Vibration of Elastic Plates with Variable Thickness on a Basis of the Refined Theories, by Natalia Chinchaladze (Speaker) at International Conference “CONTINUUM MECHANICS AND RELATED PROBLEMS OF ANALYSIS” , Tbilisi, Georgia, 09-14 September, 2011.
Cylindrical Vibration Problems for the Cusped Plates, by Natalia Chinchaladze (Speaker) at The IV Congress of the Turkic World Mathematical Society, Baku, Azerbaijan, 01-03 July, 2011.
Big deflections of the cusped plate under the Combined Action of Uniform Transverse Load and Uniform Tension, by Natalia Chinchaladze (Speaker) at International Scientific-Technical Conference “Civil Engineering Mechanics Actual Problems”, Tbilisi, Georgia, 15-17 June, 2010.
Cylindrical Vibration of Cusped Reisner-Mindlin Plates, by Natalia Chinchaladze (Speaker) at 8th AIMS Conference, Dresden, Germany, 25-28 May, 2010.
On Solid-Fluid Interaction Hierarchical Models, by George Jaiani (Speaker), Natalia Chinchaladze at 22th Enlarged Sessions of the Seminar of I.Vekua Institute of Applied Mathematics , Tbilisi, Georgia, 22-25 April, 2008.

Publications

Natalia Chinchaladze, On One Oscillation Problem of Zeroth Approximation of Hierarchical Model for Porous Elastic Plates with Variable Thickness, Trends in Mathematics, Springer, 2023.
George Jaiani, Natalia Chinchaladze, A survey of results on cusped standard and prismatic shells, in particular plates, and bars and on the corresponding singular PDEs, Continuum Mechanics and Thermodynamics, Vol. 33, pages1171–1198, Springer, 2021.
George Jaiani, Natalia Chinchaladze, Some comments on hierarchical models, Seminar of I. Vekua Institute of Applied Mathematics, REPORTS, v 47, 30-35, Tbilisi University Press, 2021.
Holm Altenbach, Natalia Chinchaladze, Reinhold Kienzler, Wolfgang Mueller, Analysis of Shells, Plates, and Beams, Sringer Series: Advanced Structured Materials, Springer, 2020.
Natalia Chinchaladze, Archil Sakevarashvili, ON A PROBLEM OF NONHOMOGENEOUS PIEZOELECTRIC ELASTIC ROD WHEN VARIABLE CONSTITUTIVE COEFFICIENTS, Lecture Notes of TICMI, Vol. 21, 121–138, Tbilisi University Press, 2020.
Natalia Chinchaladze, On a Vibration Problem of the Transversely Isotropic Bars, Bulletin of TICMI, Vol. 23(2), 87–96, Tbilisi University Press, 2019.
Natalia Chinchaladze, Robert Gilbert, On a vibration problem of antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies, Complex Variables and Elliptic Equations, Vol. 63(6), 886-895, Taylor & Francis, 2018.
Natalia Chinchaladze, Margarita tutberidze, On Some Bending Problems of Prismatic Shell with the Thickness Vanishing at Infinity, Journal of Mathematics and System Science, Vol. 7, 88-93, David Publishing Company, 2017.
Natalia Chinchaladze, George Jaiani, Antiplane strain (shear) of orthotropic nonhomogeneous prismatic shell-like bodies, Arch. Mech., Vol. 69, 4–5, pp. 305–316, IPPT PAN, 2017.
Natalia Chinchaladze, On One Problem of a Cusped Elastic Prismatic Shells in Case of the Third Model of Vekua’s Hierarchical Model, HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, Vol. 45 (6), 1665-1673, Hacettepe University, 2016.
Natalia Chinchaladze, On a Mathematical Problem of Cusped Double-Layered Plates. , PAMM, vol. 15, Issue 1, 181–182, Wiley, 2015.
Natalia Chinchaladze, On Some Dynamical Problems of the Antiplane Strain (shear) of Isotropic Non-Homogeneous Prismatic Shell-Like Bodies, Bull. TICMI, 19 (2), 55-65, Tbilisi University Press, 2015.
Natalia Chinchaladze, On a Cusped Double-layered Prismatic Shell, Proceedings of I. Vekua Institute of Applied Mathematics, v. 64, 13-23, Tbilisi University Press, 2014.
Natalia Chinchaladze, On Some Analytic Methods for Calculating of Cusped Prismatic Shells, PAMM, vol. 14, Issue 1, 185–186, Wiley, 2014.
Natalia Chinchaladze, Hierarchical Models for Biofilms Occupying Thin Prismatic Domains, Bulletin of TICMI, vol.18, No. 2, 102-109, Tbilisi University Press, 2014.
Natalia Chinchaladze, Harmonic vibration of prismatic shells in zero approximation of Vekua's hierarchical models, Applicable Analysis 92 (11), 2275-2287, Taylor and Francis Ltd., 2013.
Natalia Chinchaladze, Harmonic vibration of cusped plates in the N-th approximation of Vekua’s hierarchical models, Archives of Mechanics 65 (5), 345-365, IPPT PAN, 2013.
Natalia Chinchaladze, Robert Gilbert, George Jaiani, Sergo Kharibegashvili, David Natroshvili, Initial-boundary value problems for solid–fluid composite structures, Zeitschrift für angewandte Mathematik und Physik volume 63, pages625–653, Springer, 2012.
Natalia Chinchaladze, Harmonic vibration of a cusped plates in the first approximation of Vekua's hierarchical models, Proceedings of I. Vekua Institute of Applied Mathematics, vol. 61-62, 33-45, Tbilisi University Press, 2012.
Natalia Chinchaladze, Cylindrical bending of cusped Reisner-Mindlin plates, Dynamical Systems and Differential Equations, DCDS Supplement 2011 Proceedings of the 8th AIMS International Conference (Dresden , Germany), 282 - 291, AIMS, 2011.
Natalia Chinchaladze, George Jaiani, Boris Maistrenko, Paolo Podio-Guidugli, Concentrated contact interactions in cuspidate prismatic shell-like bodies, Archive of Applied Mechanics 81(10):1487-1505, Springer, 2011.
Natalia Chinchaladze, Robert Gilbert, George Jaiani, Sergo Kharibegashvili, David Natroshvili, Cusped Elastic Beams under the Action of Stresses and Concentrated Forces, Applicable Analysis, Volume 89, No. 5, 757–774, Taylor and Francis Ltd., 2010.
Natalia Chinchaladze, George Jaiani, Cylindrical bending of a cusped plate with big deflections, Journal of Mathematical Sciences, Volume 157, Number 1, 52-69 , Springer, 2009.
Natalia Chinchaladze, Vibration of an elastic plate under the action of an incompressible fluid, Proceedings of the IUTAM Symposium on the Relations of Shell, plate, Beam, and 3D Models Dedicated to the Centenary of Ilia Vekua's Birth, held in Tbilisi, Georgia, April 23-27,2007, 77-90, Springer, 2008.
Natalia Chinchaladze, Robert Gilbert, George Jaiani, Sergo Kharibegashvili, David Natroshvili, Existence and Uniqueness Theorems for Cusped Prismatic Shells in the N-th Hierarchical Model, Mathematical Methods in Applied Sciences, Vol. 31, No. 11, 1345-1367, Wiley, 2008.
Natalia Chinchaladze, On some nonclassical problems for differential equations and their applications to the theory of cusped prismatic shells, Lecture Notes of TICMI, v. 9, Tbilisi University Press, 2008.
Natalia Chinchaladze, Robert Gilbert, Vibration of an Elastic Plate under Action of an Incompressible Fluid in Case of N=0 Approximation of I.Vekua’s Hierarchical Models , Applicable Analysis, vol. 85, No.9, 1177-1187 , Taylor and Francis Ltd., 2006.
Natalia Chinchaladze, Robert Gilbert, Cylindrical Vibration of an Elastic Cusped Plate under Action of an Incompressible Fluid in Case of N=0 Approximation of I.Vekua’s Hierarchical Models, Complex Variables and Elliptic Equations, vol. 50, No. 7-11 , Taylor and Francis Ltd., 2005.
Giorgi Kapanadze, Natalia Chinchaladze, On a one inverse problem of the bending of a plate with variable flexural-rigidity, Seminar of I. Vekua Institute of Applied Mathematics REPORTS, Volume 31, 22-26, Tbilisi University Press, 2005.
Natalia Chinchaladze, Vibration of the plate with two cusped edges, Proceedings of I.Vekua Institute of Applied Mathematics of Tbilisi State University, vol. 52, 30-48, Tbilisi University Press, 2002.
Natalia Chinchaladze, On a Cusped Elastic Solid-Incompressible Fluid Interaction Problem. Harmonic Vibration. , Mechanics and Mechanical Engineering, vol. 6, No. 1, 5-29, Technical University of Lodz, 2002.
Natalia Chinchaladze, A cusped elastic plate-ideal incompressible fluid interaction problem, Reports of the Seminar of I.Vekua Institute of Applied Mathematics of Tbilisi State University, vol. 28, 31-39, Tbilisi University Press, 2002.
Natalia Chinchaladze, George Jaiani, On a cusped elastic solid-fluid interaction problem, AMIM, vol. 6, No. 2, 25-64, Tbilisi University Press, 2001.