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The basic publications

Vectors and
second-rank
tensors
in 3D space

Fundamental
laws of
mechanics

Applied
mechanics.
Foundations
of shells theory

Applied
mechanics.
Theory of thin
elastic rods

Theoretical
mechanics

Advansed Problems in Mechanics V. 1 (7K)

Advanced
problems
in mechanics
(vol 1)

Advansed Problems in Mechanics V. 2 (7K)

Advanced
problems
in mechanics
(vol 2)

Rational
mechanics of
continuum

Theory of ribbed shells

Zhilin P.A. Axisymmetric deformation of a cylindrical shell, supported by frames // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1966, No. 5, pp. 139 — 142. (In Russian).
Zhilin P.A., Kizima G.A. Shells of zero Gauss curvature with meridional ribs. // Trudi CKTI (Transactions of Central Boiler Turbine Institute).\ 1966.\ No. 72.\ Pp. 41 — 52. (In Russian).

On the analysis of boundary problems for ribbed shells

Zhilin P.A.General theory of ribbed shells // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1967.\ No. 6.\ P. 169. (In Russian).
Zhilin P.A., Kizima G.A. Shells of zero curvature with meridional ribs // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1967. No. 3. Pp. 102 — 105.
Zhilin P.A. General theory of ribbed shells // Trudi CKTI (Transactions of Central Boiler Turbine Institute).\ 1968. No. 88. Pp. 46 — 70. (In Russian).
Zhilin P.A., Mikheev V.I. Toroidal shell with meridional ribs for design of hydroturbine spirals. // Trudi CKTI (Transactions of Central Boiler Turbine Institute).\ 1968. No. 88. Pp. 91 — 99.
Zhilin P.A. Linear theory of ribbed shells. .Summary of PhD thesis for application to the degree of Cand.\ Sci.\ (Ph.D.) in Physical and Mathematical Sciences. Leningrad, 1968, 15 pages. (In Russian).
Zhilin P.A., Kizima G.A. Spherical collar with meridional ribs // Izvestija AN SSSR, Mekhanica tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids) 1969. №5. С. 97 — 105.
Zhilin P.A. Linear theory of ribbed shells // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1970. No. 4. Pp. 150 — 162.

Direct metod of construction of shell theory

Zhilin P.A. Mechanics of Deformable Surfaces. The Danish Center for Appl. Math and Mech. Report №89. 1975. P. 1 - 29.
Zhilin P.A. Mechanics of Deformable Cosserat Surfaces and Shell Theory. The Danish Center for Appl. Math and Mech. Annual report, 1975.
Zhilin P.A. . Mechanics of deformable enriched surfaces // Transactions of the 9th Soviet conference on the theory of shells and plates. Leningrad, Sudostroenie. 1975. Pp. 48 — 54. (In Russian).
Zhilin P.A. Mechanics of Deformable Directed Surfaces // Int. J. Solids Structures. 1976. Vol. 12. P. 635 - 648.
Zhilin P.A., Ilyicheva T.P. Spectra and forms of vibrations of a rectangular parallelepiped, obtained basing on the three-dimensional theory of elasticity and theory of plates //Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1980. No. 2. Pp. 94 — 103.
Altenbach H., Zhilin P.A. Ermitting der Steifigkeyts bezichungen fur dreisehicht schulen. // Schiffsfectigkeit und Schiffschwingungen. Heft 2. Roctoc. DDR. 1980. S. 63 — 71.
Garkavi M.A., Zhilin P.A., Rudelson V.M. Asymptotical analysis of a plane thermoelastic problem for working rolls of sheet mills // Investigation, design, and construction of machines of metallurgical industry. Symposium of research works. Moscow, VNIIMETMASH (Soviet Research Institute of Metallurgy and Mechanical Engineering) 1980. Pp. 88 — 94
Zhilin P.A., Konyushevskaya R.M., Palmov V.A., Chvartatsky R.V. On design of the stress-strain state of discharge chambers of Tokamak Panels. Leningrad, NIIEFA (Research Institute of Electro-physical apparatuses), P-OM-0550. 1982. Pp. 1 — 13. (In Russian).
Zhilin P.A. Basic equations of non-classical theory of shells // Dinamika i prochnost mashin (Dynamics and strength of machines.) Trudi LPI (Proceedings of Leningrad Polytechical Institute.) N 386. 1982. Pp. 29 — 46.
Zhilin P.A. The theory of simple shells and its applications. Summary of thesis for application to the degree of Dr.\ Sci.\ (Professor)\ in Physical and Mathematical Sciences Leningrad. 1983. 32 p.
Zhilin P.A., Skvortsov V.R. Description of a simple boundary effect in terms of the theory of shells and three-dimensional theory of elasticity // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1983. No. 5. Pp. 137 — 147. (In Russian).
Goloskokov D.P., Zhilin P.A. Equations of stability of a circular cylindrical shell under torsion // Matematicheskaya Fisika (Mathematical Physics). Intercollegiate symposium. Leningrad. 1984. Pp. 42 — 46. (In Russian).
Altenbach H., Zhilin P.A. General theory of elastic simple shells // Advances in mechanics — Warszawa, Polska. 1988. N 4. P. 107 — 148. (In Russian).
Altenbach H., Zhilin P.A. The Theory of Simple Elastic Shells // in Critical Review of The Theories of Plates and Shells and New Applications, ed. by H. Altenbach and R. Kienzler, p. 1 — 12, Berlin, Springer, 2004.
Zhilin P.A. Applied mechanics. Foundations of shells theory. Tutorial book. St. Petersburg State Polytechnical University. 2006. 167 p. (In Russian.)

Vibrations and stability of shells

Altenbach H., Zhilin P.A. Stability of a three-layer plate.Устойчивость трёхслойной полосы // Wissenschaftliche zeitschrift. Weimar. DDR. 1982. Heft 3-4. S. 265 — 267.
Altenbach H., Zhilin P.A. Die Bestimmung der Deformation senergie fur dreischichtige, orto-trope, dunner, Schalen Konstanter Dicke // Wissenschaftliche Zeitschrift der TH Otto von Guerike. Magdeburg. DDR. 26 (1982). Heft 4. S. 7 — 10.
Altenbach H., Zhilin P.A. Eine nichtlineare Theorie duner Dreischichtschalen und ihre An-wendung aufdie Stabilitatsuntersuchung eines dreischictigen Streifens // Technische Mechanic. 1982. Bd. 3. Helt 2. S. 23 — 30.
Zhilin P.A., Goloskokov D.P. Stability of a circular cylindrical shell under torsion. // Vodnie puti i portovie sooruzheniya (Waterways and port constructions). Symposium of research works of LIVT (Leningrad Institute of Water Transport), 1982. Pp. 50 — 57.
Altenbach H., Zhilin P.A. Bifurcation of an equilibrium of a three-layer plate. // Dinamika i prochnost mashin (Dynamics and strength of machines.) Trudi LPI (Proceedings of Leningrad Polytechical Institute.) No. 386. 1982. Pp. 88 — 93. (In Russian).
Zhilin P.A., Goloskokov D.P. Bifurcation of equilibrium of a thin cylindrical shell under torsion. Deposited in VINITI No. 326-83. Dep. Pp. 1— 32. (In Russian).
Goloskokov D.P., Zhilin P.A. Stability of a cylindrical shell under torsion // Vodnie puti i portovie sooruzheniya (Waterways and port constructions). Symposium of research works of LIVT (Leningrad Institute of Water Transport), 1983. Pp. 24 — 29. (In Russian).
Goloskokov D.P., Zhilin P.A. On the stability of a circular cylindrical shell under torsion // Deposited in VINITI No. 10B292 Dep. No. 4935-V87. 18 p.
Voronin I.E., Golod I.L., Zhilin P.A. Comparison of eigen-frequencies and eigen-forms for natural oscillation of a simply supported hollow cylinder obtained by 2D and 3D theories. VINITI N 7B398, N 1925 — B87. 26 p. (In Russian).

Plate theory

Zhilin P.A. Axisymmetric bending of a flexible circular plate under large displacements // Vichislitelnie metodi v mekhanike i upravlenii (Numerical methods in mechanics and control theory). Trudi LPI (Proceedings of Leningrad Polytechical Institute.) N 388. 1982. S. 97 — 106. (In Russian).
Zhilin P.A., Ilyicheva T.P. Analysis of applicability of Timoshenko-type theory for the case of a plate under concentrated load // Prikladnaya Mekhanika i Tekhnicheskaya Fisika SO AN SSSR (Applied Mathematics and Technical Physics). 1984. No. 1. Pp. 150 — 156. (In Russian).
Zhilin P.A. Axisymmetrical bending of a circular plate under large displacements //Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1984. No. 3. Pp. 138 — 144. (In Russian).
Zhilin P.A. . The view on Poisson's and Kirchhoff's theories of plates in terms of modern theory of plates // Izvestia RAN. Mechanika Tverdogo Tela (Mechanics of Solids). 1992. N 3. P. 48 — 64. (In Russian). // Izvestia RAN. Mechanika Tverdogo Tela (Mechanics of Solids). 1992. N 3. P. 48 — 64. (In Russian).
Zhilin P.A. Ivanova E.A. Modified functional of energy in the theory of shells of the Reissner type // Izvestia RAN. Mechanika Tverdogo Tela (Mechanics of Solids). 1995. N 2. P. 120 — 128. (In Russian).
Zhilin P.A. On the classical theory of plates and the Kelvin-Teit transformation // Izvestia RAN. Mechanika Tverdogo Tela (Mechanics of Solids). 1995. N 4. P. 133 — 140. (In Russian).

Theory of rods

Goloskokov D.P., Zhilin P.A. General nonlinear theory of elastic rods with application to the description of the Pointing effect // Deposited in VINITI No. 1912 — B87. Dep. 20 p. (In Russian).
Zhilin P.A., Sergeyev A.D. Twisting of an elastic cantilever rod by a torque subjected at a free end. St. Petersburg State Technical University. 1993. 32 p. (In Russian).
Zhilin P.A., Sergeyev A.D. Experimental investigation of the stability of a cantilever rod under torsion deforming // Mechanics and Control. Proc.\ of St. Petersburg State Technical University. 1993. N 446. P. 174 — 175. (In Russian).
Zhilin P.A., Sergeyev A.D. Equilibrium and stability of a thin rod subjected to a conservative moment // Mechanics and Control. Proc.\ of St. Petersburg State Technical University. 1994. N 448. P. 47 — 56. (In Russian).
Zhilin P.A. Spin motions and stability of equilibrium configurations of thin elastic rods // Mechanics and Control. Proc.\ of St. Petersburg State Technical University. 1995. N 458. P. 56 — 73. (In Russian).
Zhilin P.A., Sergeyev A.D., Tovstik T.P. Nonlinear theory of rods and its application . // Proc.\ of XXIV Summer School — Seminar “Nonlinear Oscillations in Mechanical Systems”. St. Petersburg. 1997. P. 313 — 337. (In Russian).
Zhilin P.A. Dynamic Forms of Equilibrium Bar Compressed by a Dead Force // Proc. of 1997 1st Int. Conf. Control of Oscillations and Chaos. Vol. 3. P. 399 - 402.
Zhilin P.A.Applied mechanics. Theory of thin elastic rods. Tutorial book. St. Petersburg State Polytechnical University. 2007. 101 p. (In Russian.)

Tensor calculus

item Goloskokov D.P., Zhilin P.A. Applications of tensor calculus // Ministerstvo rechnogo flota RSFSR, LIVT (Ministry of the river fleet of the Russian Federation, Leningrad Institute of the Water Transport). Leningrad. 1988. 62 p. (In Russian).
Zhilin P.A. Vectors and second-rank tensors in three-dimensional space. St. Petersburg State Technical University. 1992. 86 p. (In Russian).
Zhilin P.A. Vectors and second-rank tensors in three-dimensional space. St. Petersburg: Nestor. 2001. 276 p.
Zhilin P.A. Modified theory of symmetry for tensors and their invariants // Izvestiya VUZov. Severo-Kavkazskii region. Estestvennye nauki (Transactions of Universities. South of Russia. Natural sciences). Special issue “ Nonlinear Problems of Continuum Mechanics ”. 2003. P 176 — 195. (In Russian).
Zhilin P.A. Symmetries and Orthogonal Invariants in Oriented Space // Proceedings of XXXII Summer School - Conference “Advanced Problems in Mechanics”. St. Petersburg, Russia. 2005. P. 470-483.
Altenbach H., Naumenko K., Zhilin P.A. A note on transversely-isotropic invariants // ZAMM. Z. Angew. Math. Mech. 86, №2. P. 162–168. (2006)

Rigid body of dinamics

Zhilin P.A. The turn-tensor in kinematics of a rigid body // Mechanics and Control. Proc.\ of St. Petersburg State Technical University. 1992. N 443. P. 100 — 121. (In Russian).
Zhilin P.A., Zhilina O.P. On the Coulomb's laws of friction and the Painlev\'e paradoxes // Mechanics and Control. Proc.\ of St. Petersburg State Technical University. 1993. N 446. P. 52 — 81. (In Russian).
Zhilin P.A. New results concerning the analysis of free rotation of rigid bodies. IPME RAS. Preprint N 102. 1994. 34 p. (In Russian).
Zhilin P.A., Tovstik T.P. Rotation of a rigid body based on an inertial rod // Mechanics and Control. Proc.\ of St. Petersburg State Technical University. 1995. N 458. P. 78 — 83. (In Russian).
Zhilin P.A. A New Approach to the Analysis of Free Rotations of Rigid Bodies // ZAMM Z. angew. Math. Mech. 76 (1996). Vol. 4. P.187 — 204.
Zhilin P.A. Rotations of Rigid Body with Small Angles of Nutation // ZAMM. Z. angew. Math. Mech. 76, (1996). S. 2. P. 711 — 712.
Zhilin P.A. Dynamics and stability of equilibrium positions of a rigid body on an elastic foundation . // Proc.\ of XXIV Summer School — Seminar “ Nonlinear Oscillations in Mechanical Systems ”. St. Petersburg. 1997. P. 90 — 122. (In Russian).
Zhilin P.A., Sorokin S.A. . Multi-rotor gyrostat on a nonlinear elastic foundation // IPME RAS. Preprint N 140. 1997. 83 p. (In Russian).
Zhilin P.A. A General Model of Rigid Body Oscillator // Nonlinear Oscillations in Mechanical Systems: Proc. of the XXV-XXIV Summer Schools. Vol. 1. St. Petersburg. 1998. P. 288 — 314.
Zhilina O.P.; Zhilin P.A. One Peculiarity of the Problems with Coulomb Friction // Nonlinear Oscillations in Mechanical Systems: Proc. of the XXV-XXIV Summer Schools. Vol. 1. St. Petersburg. 1998. P. 315 — 320.
Zhilin P.A., Sorokin S.A. The Motion of Gyrostat on Nonlinear Elastic Foundation // ZAMM. Z. Angew. Math. Mech. 78, (1998), S2. S. 837 — 838.
Zhilin P.A. Dynamics of the two rotors gyrostat on a nonlinear elastic foundation // ZAMM. Z. Angew. Math. Mech. 79, (1999), S2. S. 399 — 400.
Wiercigroch M., Zhilin P.A. On the Painleve Paradoxes // Nonlinear Oscillations in Mechanical Systems: Proc. of the XXVII Summer Schools. St. Petersburg. 2000. P. 1 — 22.
Zhilin P.A. Rigid body oscillator: a general model and some results // Acta Mechanica. Vol. 142. P. 169 — 193. (2000).
Ivanova E.A., Zhilin P.A. Non-stationary regime of the motion of a rigid body on an elastic plate // Proc.\ of XXIX Summer School — Conference “ Advanced Problems in Mechanics”. St. Petersburg. 2002. P. 357 — 363.

Fundamental laws of mechanics

Zhilin P.A. Main structures and laws of rational mechanics // Proc.\ of the 1st Soviet Union Meeting for Heads of Departments of Theoretical Mechanics. St. Petersburg: VIKI. 1994. P. 23 — 45. (In Russian).
Zhilin P.A. Basic concepts and fundamental laws of rational mechanics // Proc.\ of XXII Summer School — Seminar “Nonlinear Oscillations in Mechanical Systems”. St. Petersburg. 1995. P. 10 — 36. (In Russian).
Zhilin P.A. . Theoretical mechanics. . Tutorial book. St. Petersburg State Polytechnical University. 2001. 146 p. (In Russian).
Zhilin P.A. Basic postulates of the Eulerian mechanics //Proc.\ of XXIX Summer School — Conference “ Advanced Problems in Mechanics”. St. Petersburg. 2002. P. 641 — 675. (In Russian)
Zhilin P.A. Theoretical mechanics. Fundamental laws of mechanics. Tutorial book. St. Petersburg State Polytechnical University. 2003. 340 p. (In Russian).

Electrodynamics and the quantum mechanics

Zhilin Galileo's equivalence principle and Maxwell's equations St. Petersburg State Technical University. 1993. 40 p. (In Russian).
Galileo's equivalence principle and Maxwell's equations // Mechanics and Control. Proc.\ of St. Petersburg State Technical University. 1994. N 448. P. 3 — 38. (In Russian).
Zhilin Reality and mechanics // // Proc.\ of XXIII Summer School — Seminar “ Nonlinear Oscillations in Mechanical Systems”. St. Petersburg. 1996. P. 6 — 49. (In Russian).
Zhilin P.A. Classical and Modified Electrodynamics // New Ideas in Natural Sciences. Int. Conf. St. Petersburg, June 17-22, 1996. Part I - Physics. P. 73 — 82.
Zhilin P.A. Classical and Modified Electrodynamics // Problems of Space, Time and Motion. Int. Conf. dedicated to the 350th anniversary of Leibniz. St. Petersburg. 1997. Vol. 2. P. 29 — 42.
Zhilin P.A. The Main Direction of the Development of Mechanics for XXI century // Lecture at XXVIII Summer School - Conference “Advanced Problems in Mechanics ”. (In book: Zhilin P.A. Advanced Problems in mechanics. Selection of articles. Vol. 2. St. Petersburg. Edition of IPME RAS. 2006. 271 p.)
Ivanova E.A., Krivtsov A.M., Zhilin P.A. Description of rotational molecular spectra by means of an approach based on rational mechanics // ZAMM. Z. Angew. Math. Mech. 87. № 2. P. 139 — 149. (2007)

The general theory of inelastic media

Krivtsov A.M., Zhilin P.A. Computer simulation of large inelastic deformations. VINITI. 1997. N 1344-B97. 11 p. (In Russian).
Krivtsov A.M., Zhilin P.A. Particle Simulation of Large Inelastic Deformations. // Transactions of the 14th International Conference on Structural Mechanics in Reactor technology (SMiRT 14). Lyon. France. August 17 - 22, 1997. P. 121 — 128.
Zhilin P.A. Basic equations of the theory of non-elastic media // Proc.\ of the XXVIII Summer School “ Actual Problems in Mechanics”. St. Petersburg. 2001. P. 14 — 58. (In Russian).
Zhilin P.A. Phase Transitions and General Theory of Elasto-Plastic Bodies // // Proc.\ of XXIX Summer School “ Advanced Problems in Mechanics”. St. Petersburg. 2002. P. 36 — 48.
Altenbach H., Naumenko K., Zhilin P. A micro-polar theory for binary media with application to phase-transitional flow of fiber suspensions // Continuum Mechanics and Thermodynamics, 2003г. Vol. 15, № 6. P. 539 — 570.
Altenbach H., Naumenko K., Zhilin P.A. A micro-polar theory for binary media with application to flow of fiber suspensions // Proceedings of XXX Summer School - Conference “Advanced Problems in Mechanics”. St. Petersburg, Russia, 2003. P. 39 — 62.
Zhilin P.A. Mathematical theory of non-elastic media // Uspehi mechaniki (Advances in mechanics). Vol. 2. N 4. 2003. P. 3 — 36. (In Russian).
Zhilin P.A. On the general theory of non-elastic media // Mechanics of materials and strength of constructions. Proc.\ of St. Petersburg State Polytechnical University. N~489. 2004. P. 8 — 27. (In Russian).

Piezoelasticity

Zhilin P.A., Vekovischeva I.A., Than Ti Ahn. Free transversal oscillation of a piezoelectric plate with clamped boundary // Mechanics and Control. Proc.\ of St. Petersburg State Technical University. 1995. N458. P.50 — 56. (In Russian).
Kolpakov Ja. E., Zhilin P.A. Generalized continuum and linear theory of the piezoelectric materials //Proc.\ of XXIX Summer School — Conference “ Advanced Problems in Mechanics”. St. Petersburg. 2002. P. 36 — 48.
Zhilin P.A., Kolpakov Ya.E. A micro-polar theory for piezoelectric materials // Lecture at XXXIII Summer School — Conference “Advanced Problems in Mechanics”, St. Petersburg, Russia, 2005.

Ferromagnetism

Grekova E.F., Zhilin P.A. Ferromagnets and Kelvin's Medium: Basic Equations and Magneto-acoustic Resonance // Nonlinear Oscillations in Mechanical Systems. Proc. of the XXV-XXIV Summer Schools. Vol. 1. St.-Petersburg, 1998. P. 259 — 281.
E.F. Grekova and P.A. Zhilin. Kelvin's medium and ferromagnets: constitutive equations and wave processes // Nonlinear Acoustics of Solids: Proc. of VIII Session of the Russian Acoustical Society. Nizhniy Novgorod. Russia. 1998. P. 87 — 90.
Grekova E.F., Zhilin P.A. On the choice of strain tensors for magnetic materials and mechanical polar media // Nonlinear Oscillations in Mechanical Systems: Proc. of the XXVII Summer Schools. St. Petersburg. 2000. P. 231 — 242.
Grekova E.F., Zhilin P.A. Equations for non-linear elastic polar media and analogies: Kelvin medium, non-classical shells, and ferromagnetic insulators // Izvestiya VUZov. Severo-Kavkazskii region. Estestvennye nauki (Transactions of Universities. South of Russia. Natural sciences). Special issue “ Nonlinear Problems of Continuum Mechanics”. 2000. P 24 — 46. (In Russian).
Grekova E.F., Zhilin P.A. On the choice of strain tensor for nonlinear polar media, hypothesis of natural state, and linearization // Actual Problems in Mechanics: Proc. of the XXVIII Summer Schools. St. Petersburg. 2001. P. 59 70.
Grekova E.F. and Zhilin P.A. Basic equations of Kelvin's medium and analogy with ferromagnets // Journal of elasticity. Vol. 64. P. 29 — 70. (2001).

Miscellaneous

Zhilin P.A., Lurie A.I. . Editorial preface to the translation of the book: C. Truesdell “A first course in rational continuum mechanics”. Moscow, Mir. 1975. Pp. 5 — 7.
Zhilin P.A. Education and the future of Russia // MOST (Informational and analytical journal for manufacturers). 1999. N 25. P. 44 — 46. (In Russian).
Zhilin P.A. A.I. Lurie's studies of mechanics // Proc.\ of the XXVIII Summer School “ Actual Problems in Mechanics ” . St. Petersburg. 2001. P. 1 — 13. (In Russian).
Zhilin P.A. Advanced problems in mechanics. Theory of thin elastic rods.// Selection of articles. V. 1. St. Petersburg. Edition of IPME RAS. 2006. 306 p.
Zhilin P.A. Advanced problems in mechanics. Nonlinear Theory of Thin Rods.// Selection of articles. V. 2. St. Petersburg. Edition of IPME RAS. 2006. 271 p.