Compatibility Equations in the Theory of Elasticity

[+] Author and Article Information
Igor V. Andrianov

Institute of General Mechanics, RWTH Aachen, Templergraben 64, Aachen, D-52062, Germany

Jan Awrejcewicz

Department of Automatics and Biomechanics, Technical University of Łódź, 1/15 Stefanowski St., 90-924 Łódź, Poland

J. Vib. Acoust 125(2), 244-245 (Apr 01, 2003) (2 pages) doi:10.1115/1.1547681 History: Received March 01, 2001; Revised October 01, 2002; Online April 01, 2003
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.


Borodachev,  N. M., 1995, “About One Approach in the Solution of 3D Problem of the Elasticity in Stresses,” Int. J. Appl. Mech., 31(12), pp. 38–44.
Vasil’yev,  V. V., and Fedorov,  L. V., 1996, “To the Problem of the Theory of Elasticity, Formulated in Stresses,” Mech. Solids, 31(2), pp. 82–92.
Pobedrya, B. Ye., Sheshenin, S. V., and Holmatov, T., 1988, Problem in Stresses, Tashkent, Fan (in Russian).
Awrejcewicz, J., and Krys’ko, V. A., 2002, Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells, Springer-Verlag, Berlin.
Ostrosablin,  N. I., 1997, “Compatibility Equations of Small Deformations and Stress Functions,” J. Appl. Mech. Tech. Phys., 38(5), pp. 774–783.
Nowacki, W., 1975, Theory of Elasticity, Mir, Moscow (in Russian).
Germain, P., 1962, Mecanique des Mileux Cintinus Massonerice, Editeurs, Paris.
Amenzade, Yu. A., Theory of Elasticity, Mir, Moscow.
Donnel, L. H., 1976, Beams, Plates and Shells, McGraw-Hill, New York.
Christensen, R. M., 1979, Mechanics of Composite Materials, John Wiley and Sons, New York.
Hahn, H. G., 1985, Elastizita Theorie Grundlagen der Linearen Theorie und Anwendungen auf undimensionale, ebene und zäumliche Probleme, B. G. Teubner, Stuttgart.
Rabotnov, Yu. N., 1979, Mechanics of Deformable Rigid Body, Nauka, Moscow (in Russian).
Zubchaninov, V. P., 1990, Foundation of the Theory of Elasticity and Plasticity, Vishaya Shcola, Moscow (in Russian).
Trefftz, E., 1928, “Mechanik der elastischen Körper,” Handbuch der Physik, VI, Berlin.
Krutkov, Yu. A., 1949, Tensor of the Function of Stresses and General Solutions in the Statical Theory of Elasticity, AN USSR, Moscow-Leningrad (in Russian).
Timoshenko, S. P., and Goodier, J. N., 1954, Theory of Elasticity, McGraw-Hill, New York.
Terebushko, O. I., 1984, Foundations of the Theory of Elasticity and Plasticity, Nauka, Moscow (in Russian).
Lihachev, V. A., and Fleyshman, N. P., 1984, Beltrami-Michell Equations of Compatibility, Doklady AN USSR, A(9), pp. 45–47 (in Russian).
Belov,  P. A., Yelpat’yevskiy,  A. N., and Lur’ye,  S. A., 1980, “To General Solution of the Theory of Elasticity in Stresses,” Strength of Constructions, 4, pp. 159–163 (in Russian).
Maliy,  V. I., 1987, “Independent Conditions of Stress Compatibility for Elastic Isotropic Body,” Doklady AN USSR, A(7), pp. 43–46 (in Russian).
Pobedrya, B. Ye., 1981, Numerical Methods in the Theory of Elasticity and Plasticity, MGU, Moscow, (in Russian).
Kozak,  J., 1980, “Notes on the Field Equations with Stresses and on the Boundary Conditions in the Linearized Theory of Elastostatics,” Acta Technica Acad. Sci. Hung., 90(3–4), pp. 221–245.
Gol’denveizer, A. L., 1961, Theory of Elastic Thin Shells, Pergamon Press, New York.
Levi,  E. E., 1907, “Sulle equazioni lineari totalmente elliptiche alle derivate parziali,” Rendiconti del Circolo Matematico di Palermo, 24, pp. 275–317.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In