It is shown by operational method that the boundary value problem of the theory of elasticity related to stresses, which can be reduced to three strains compatibility equations and to three equilibrium equations, in fact is of sixth order. Hence, it is not required to formulate additional boundary conditions.

1.
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
.
2.
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
.
3.
Pobedrya, B. Ye., Sheshenin, S. V., and Holmatov, T., 1988, Problem in Stresses, Tashkent, Fan (in Russian).
4.
Awrejcewicz, J., and Krys’ko, V. A., 2002, Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells, Springer-Verlag, Berlin.
5.
Ostrosablin
,
N. I.
,
1997
, “
Compatibility Equations of Small Deformations and Stress Functions
,”
J. Appl. Mech. Tech. Phys.
,
38
(
5
), pp.
774
783
.
6.
Nowacki, W., 1975, Theory of Elasticity, Mir, Moscow (in Russian).
7.
Germain, P., 1962, Mecanique des Mileux Cintinus Massonerice, Editeurs, Paris.
8.
Amenzade, Yu. A., Theory of Elasticity, Mir, Moscow.
9.
Donnel, L. H., 1976, Beams, Plates and Shells, McGraw-Hill, New York.
10.
Christensen, R. M., 1979, Mechanics of Composite Materials, John Wiley and Sons, New York.
11.
Hahn, H. G., 1985, Elastizita Theorie Grundlagen der Linearen Theorie und Anwendungen auf undimensionale, ebene und za¨umliche Probleme, B. G. Teubner, Stuttgart.
12.
Rabotnov, Yu. N., 1979, Mechanics of Deformable Rigid Body, Nauka, Moscow (in Russian).
13.
Zubchaninov, V. P., 1990, Foundation of the Theory of Elasticity and Plasticity, Vishaya Shcola, Moscow (in Russian).
14.
Trefftz, E., 1928, “Mechanik der elastischen Ko¨rper,” Handbuch der Physik, VI, Berlin.
15.
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).
16.
Timoshenko, S. P., and Goodier, J. N., 1954, Theory of Elasticity, McGraw-Hill, New York.
17.
Terebushko, O. I., 1984, Foundations of the Theory of Elasticity and Plasticity, Nauka, Moscow (in Russian).
18.
Lihachev, V. A., and Fleyshman, N. P., 1984, Beltrami-Michell Equations of Compatibility, Doklady AN USSR, A(9), pp. 45–47 (in Russian).
19.
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).
20.
Maliy
,
V. I.
,
1987
, “
Independent Conditions of Stress Compatibility for Elastic Isotropic Body
,”
Doklady AN USSR
,
A
(
7
), pp.
43
46
(in Russian).
21.
Pobedrya, B. Ye., 1981, Numerical Methods in the Theory of Elasticity and Plasticity, MGU, Moscow, (in Russian).
22.
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
.
23.
Gol’denveizer, A. L., 1961, Theory of Elastic Thin Shells, Pergamon Press, New York.
24.
Levi
,
E. E.
,
1907
, “
Sulle equazioni lineari totalmente elliptiche alle derivate parziali
,”
Rendiconti del Circolo Matematico di Palermo
,
24
, pp.
275
317
.
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