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\begin{center}  {\bf ANDREJ V. CHERKAEV} \\
 

{\bf LIST of PUBLICATIONS }\footnote{The conference abstracts etc. minor publications are not included in the list.}
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\begin{thebibliography}{999} 


   
\bibitem{ch1} On applying Prager`s theorem to the problems of optimal design of thin plates. - Mechanics of Solids (Izv. Acad. Sci. USSR, MTT), 1976, N.6, pp. 157-159. K.Lurie - coauthor. 

 


\bibitem{ch2} On the problem  of formulating the problem of optimal design of freely  oscillating structures.- PMM (J. Appl. Math.and Mech.), 1978, 42, N.1, pp. 194-197.

 


\bibitem{ch3} On solution of problems of optimization of eigenvalues in designing elastic constructions. - Mechanics of Solids (Izv. Acad. Sci. USSR, MTT), 1978, J.-L.Armand, K.A.Lurie - coauthors. 

 


\bibitem{ch4} Inhomogeneous bar of extremal torsional rigidity.- in: Nonlinear problems of engineering mechanics. Optimization of constructions, Kiev, 1978. pp. 80-89. K.Lurie - coauthor. (in Russian)

 


\bibitem{ch5} On the optimal form of an axis of an elastic curved bar. - in: Methods and facilities of mathematical modeling, Alma-Ata, pp. 87-93. Yu.Bulatov - coauthor. (in Russian)

 

\bibitem{ch6} Some problems of optimal design of elements of elastic structures. - Ph.D. Thesis, 130p., 1979. (in Russian)

 

\bibitem{ch8} Non-homogeneous bar  of extremal torsional rigidity. - Mechanics of Solids (Izv. Acad. Sci.), 1980, N.6. N.Lavrov, K.Lurie - coauthors.

 

\bibitem{ch9} On limiting facilities of design of elastic plates. - Proceedings of XII All-Union Conference on theory plates and shells, Yerevan, 1980, v. 3, pp.  25-30. K.Lurie, A.Fedorov - coauthors. (in Russian)

 
 
 


\bibitem{ch10}~~ Regularization of optimal problems of design of bars and plates  and solving the contradictions in a system of necessary conditions of optimality.   J. Opt.  Theory  Appl. , 1982, v. 37, N. 4,  pp.  499-522 (part 1), 523-542 (part 2). K.Lurie, A.Fedorov - coauthors. 

The preliminary version of two parts of the last paper has been earlier published  separately in Russian  as:

*  Regularization of optimal problems of design of bars and plates  and solving the contradictions in a system of necessary conditions of optimality. - Report N. 667, Phys.-Tech. Inst. Acad. Sci. USSR, 1980, 60 pp.  (in Russian)   

and

* On existence of the solutions of some problems of optimal design of bars and plates.- Report N. 668, Phys.-Tech. Inst. Acad. Sci. USSR., 1980, 43 pp.  (in Russian)   
 


\bibitem{ch12} Sliding regimes and anisotropy in optimal design of vibrating axisymmetric plates.   Int. J. of Solids and Structures, 1981, 17, No. 10, pp.  931-948. N.Olhoff, K.Lurie, A.Fedorov - coauthors. 

Preliminary version has been published as: 

* Report N. 192, The Technical University of Denmark, 1980, 34 pp.  
 

\bibitem{ch13} Editor's supplement to the Russian translation of the book by N.Olhoff ``Optimal design of elastic construction elements (problems of vibration and loss of stability)"  M. Mir, 1981. 16p. K.Lurie - coauthor. (in Russian)

 
 

\bibitem{ch15} Exact estimates of conductivity of mixtures composed of two materials taken in prescribed proportion (plane problem).- Doklady Akademii Nauk  SSSR, 1982, 264, N.5, pp. 1128-1130. K.Lurie - coauthor. 

 

\bibitem{ch16} Exact estimates of conductivity of mixtures composed of two isotropic media taken in prescribed proportion. Proceed. Roy. Soc. Edinburgh.,sect. A, 1984, 99 (P1-2), pp. 71-87. K.Lurie - coauthor.

The preliminary version of the last paper has been published in Russian in 1982 as as:

* Report 783, Phys.-Tech. Inst. Acad. Sci. USSR, 1982, 32p. (in Russian);  K.Lurie - coauthor.


 

\bibitem{ch17} Choosing of optimal orientation of axes of elastic symmetry of orthotropic plate. - Mech. Solids, (Izv. Acad. Sci. USSR, MTT) ,1983, No.3, pp. 135-142. A.Fedorov - coauthor.

 
 

\bibitem{ch19} G-closure of a set of  conducting media (  two-dimensional problem). -  Doklady Akademii Nauk  SSSR, 1981, 259, N.2, pp. 238-241. K.Lurie - coauthor.

 
\bibitem{ch19*} G-closure of a set of anisotropic conducting media in the two-dimensional case.  J. Opt. Theory Appl. , 1984, 42, N.2, pp. 283-304. K.Lurie - coauthor.


\bibitem{ch20} G-closure of some particular sets of admissible material characteristics for the problem of bending of the thin elastic plates. J. Opt. Theory Appl. , 1984, 42, N.2, pp.  305-316. K.Lurie - coauthor.  

 
The preliminary version of the last paper has been published  as:

* Report N. 213, The Technical University of Denmark, 1981, 18 pp.; J. Opt. Theory Appl. , 1984, 42, N.2, pp.  305-316.  


\bibitem{ch21} Optimal control theory and structural design. - In: New directions in optimal structural design, H.Atreck, R.H.Gallagher, O.C.Zienkewicz eds., Wiley, 1984, pp. 211-229. J.-L.Armand, K.A.Lurie - coauthors.

 

\bibitem{ch22} Optimal design of composite plates.- Proceedings of All-Union Conference ``Problems of reduction of specific consumption of materials of load-bearing units". Gorkij, 1984, pp.  27-28. L.Gibiansky - coauthor. (in Russian)

 
\bibitem{ch23} Exact estimates of conductivity of a binary mixture of isotropic compounds.  Proceedings R. Soc. Edinburgh, sect. A, 1986, 104 (P1-2), pp.  21-38. K.Lurie - coauthor. 

  
The preliminary version of the last paper has been published in Russian in 1984  as:

* Report N.894, Phys.-Tech. Inst. Acad. Sci. USSR, 1984, 26 pp.

\bibitem{ch24} The problem of formation of an optimal isotropic multicomponent composite. - Report No. 895, Phys.-Tech. Inst. Acad. Sci. USSR, 1984, 32 pp.  (in Russian)


\bibitem{ch25} Optimal design of elastic bodies and the problem of regularization. - Dynamics and strength of mechanisms, 1984, No. 40/80, pp.  25-31. K.Lurie - coauthor. (in Russian)

 

\bibitem{ch26} Effective characteristics of composites and problems of optimal design. - Advances of mathematical sciences, 1984, v.39, N.4(238), pp. 122. K.Lurie - coauthor.  (in Russian).

 English translation  in:  
Topics in the mathematical modelling of composite materials, R.Kohn  
editor, Birkhausen, NY, 1994.


 

\bibitem{ch27} Design of composite plates of extremal rigidity.- Report 914. Phys.-Tech. Inst. Acad. Sci. USSR, Leningrad,1984, 60 pp.  L.Gibiansky - coauthor. (in Russian).

 English translation  in:  
Topics in the mathematical modelling of composite materials, R.Kohn  
editor, Birkhausen, NY, 1994.

 

\bibitem{ch28} Exact estimates of energy of deformation of elastic composite plates; application to the problems of optimal design. - Proceedings of II All-Union ``Strength, rigidity and adaptability to manufacture structures from composite materials", Yerevan, 1984, v.1, pp.  171-176. L.Gibiansky - coauthor. (in Russian)

 

\bibitem{ch29} Method of deriving the exact estimates of effective constants of composites.- Problems of nonlinear mechanics of continuous medium, 1985, Tallin, pp. 63-72. K.Lurie - coauthor. (in Russian)

 
 

\bibitem{ch33} A hole in a plate, optimal for its biaxial extension compression.- PMM J. Appl.Math.and Mech., 1986, v.50, N.3, pp. 401-404. S.B.Vigdergauz - coauthor.

 
 

\bibitem{ch35} Optimization of properties of multicomponent isotropic composites. - J. Optim. Theory and Applic., 1985, 46, N.4, pp. 571-580. K.Lurie - coauthor.

 

\bibitem{ch36} Optimum focusing of heat flux by means of a non-homogeneous heat conducting medium. - Report 305, The Technical University of Denmark, 1985. 11 pp.  L.Gibiansky,K.Lurie - coauthors.
 

 

\bibitem{ch39} Relaxation of non-convex multidimensional problems by means of constructing quasi-convex envelopes.- Advances of mathematical sciences, 1986, v. 41, No. 4 (250). (in Russian)

  

\bibitem{ch41} Microstructures of composites of extremal rigidity and exact estimates of provided energy density. - Report 1115. Phys.-Tech. Inst. Acad. Sci. USSR, Leningrad, 1987. L.Gibiansky - coauthor. (in Russian) .

    English translation  in:  
Topics in the mathematical modelling of composite materials, R.Kohn  
editor, Birkhausen, NY, 1994.



\bibitem{ch42} Optimal Distribution of Viscoelastic Materials in Axisymmetric Constructions. - Report N.1116, Phys.-Tech. Inst. Acad. Sci. USSR,  Leningrad, 1987, 41 pp.  L.Gibiansky, Ju. Malinin - coauthors.(in Russian)

 

\bibitem{ch44} Dynamic head of loud-speaker.- Author's certificate N1304177 of 12.15.1986.  pp. Melnic, T.Romanova, I.Poljakova, A.Mjagy - coauthors. (in Russian)

 

\bibitem{ch45} Optimal design of nonlinear-elastic and plastic-elastic  bars under torsion. - Mechanics of solids ( Izv. Acad. Sci. USSR, MTT), 1988, N. 5, pp. 168-174. L.Gibiansky - coauthor.

 

\bibitem{ch46} Optimal focusing of heat flow by heterogeneous heat-conducting media (thermo-lens problem). - J. Techn. Phys. (Zh. Tech. Fiz.) Acad. Sci. USSR, 1988, 58, N.1, pp.  67-74. K.Lurie, L.Gibiansky - coauthors.

 

\bibitem{ch47} On the effective conductivity of polycrystals and a 3-dimensional phase-interchange inequality.- J. Appl. Phys., 1988, 63, N.10, 4989-5003. M.Avellaneda, K.Lurie, G.Milton - coauthors.

 

\bibitem{ch48} The set of tensor pairs of dielectric and magnetic permeabilities of two-phase composites.- Report N. 1286, Phys.-Tech. Inst. Acad. Sci. USSR, 1988, 51 pp.  L.Gibiansky - coauthor. (in Russian) 


 

\bibitem{ch49} Optimization the structure of inhomogeneous bodies by variational methods. - Dissertation for degree ``Doctor of Physics and Mathematics". Leningrad State University, 1988. 330 pp. (in Russian)

 

\bibitem{ch50} On a certain variational problem of phase equilibrium. In: Material Instabilities in Continuum Mechanics and Related Mathematical Problems, ed. by J. Ball, Clarendon Press, Oxford, 1988, pp.257-268. K.Lurie - coauthor.

 

\bibitem{ch51} Conductivity of polycrystals and a phase interchange inequality.- Physica A, 1989, 157, N.1, pp. 148-153. M.Avellaneda, K.Lurie, G.Milton - coauthors.

 

\bibitem{ch52} Membrane-surface forms during local change of surface-energy applications to endocytosis processes.- Biologicheskie membrany, 7, No. 3, 1990 pp.  326-334. L.Gibiansky, V.Serikov N. Serikova, Yu Malinin - coauthors.(in Russian)

 

\bibitem{ch53} On the optimization of rigidity of an elastic construction. - Proceedings of Leningrad Shipbuilding Inst. Seria ``Applied Mathematics". 1990, pp.25-34. (in Russian)


 

\bibitem{ch54} The exact coupled bounds for effective tensors of electrical and magnetic properties of two-component two-dimensional composites. 42 pp.   -  Proceed. of Royal Soc. of Edinburgh, (1992) v, 122A, pp. 93-125 . L.Gibiansky - coauthor.

 

\bibitem{ch55} Coupled estimates for the bulk and shear moluli of a two-dimensional isotropic elastic composite. J.Mech. Phys. Solids 41 (5), 937-980, 1993.  L.Gibiansky - coauthor.




 

\bibitem{ch56} Improving the Hashin-Strickman estimates by means of the translation method. - Proceedings of SIAM workshop in micromechanics. Leesburgh, Virginia,
  1991. L.Gibiansky - coauthor.

 


\bibitem{ch58} Invariant properties of the stress  in plane elasticity and equivalence classes of composites. Proc R.Soc. Lond. A (1992), v. 438, pp. 519-529.  G.W.Milton and K.A.Lurie - coauthors.

 


\bibitem{ch60} Stability of optimal structures of elastic composites.  In: Topology Design of Structures.  M.Bendsoe and C.A.Mota Soares - editors. p. 547-558, Kluwer, 1992.

 

\bibitem{ch62} Conducting and Elastic Composites of Optimal Structures. In: Structural Optimization 93, J.Herskopvits - ed., vol. 1, pp. 377- 385. ABCM, Brazil, 1993

 

\bibitem{ch61}
Variational principles  
for  complex conductivity, viscoelasticity  and similar problems  
in media with complex moduli. L.Gibiansky - coathor.  J. of Math. Physics 35 
(1), pp. 1-19, 1994

 

\bibitem{ch66} Relaxation of  problems of optimal structural design.  Int. J. of Solids and Structures 31, N0 16, pp 2251-2280, 1984.

\bibitem{ch67} Reducing of optimal design problems to the minimal variational problem. 34 pp. Submitted to:  Proceedings of the second Workshop on Composite 
Media and Homogenization in Trieste. Dal Maso- editor. 


\bibitem{ch68} Extremal structures of multiphase composites.  L.Gibiansky - coathor. 21 pp. Submitted to J. of Applied Physics. 


\bibitem{ch65} Waiting element structures and stability under extension. L. Slepyan -coauthor. 18 pp. Submitted to J. of Appl. Mechanics. 


\bibitem{ch69} Optimal design of Three-Dimensional Axisymmetric Structures. R.Palais - coauthor. 27 pp. Accepted in Int. J. of Structural optimization. 


\bibitem{ch59}  Complete characterization of possible isotropic effective tensors of polycrystals in planar elastisity (othotropic monocrystal). In progress.  M. Avellaneda, L.Gibiansky,  G.W.Milton and - coauthors.

\bibitem{ch60}  Optimization of Elastic Structures.   Axisymmetric  Problem.
R.Palais - coauthor. Submitted. Invited paper for the volume `Advanced in Engineering' edited by Leondes. 


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