**28**, 4, pp. 635–652, 1980

### An analysis of various descriptions of state of strain in the linear Kirchhoff-Love type shell theory

In the first part of the paper several methods of describing the state of strain in the thin shell with Kirchhoff-Love constraints are discussed. Among others Kilchevsky's idea of the description of the state of strain in an arbitrary point of the shell is presented by means of the strain tensor parallely shifted to the base on the middle surface. Attention has been called to the physical meaning of Kilchevsky's tensor. Two forms of solving the parallel shift problem, i.e. "operator" equations and generalized Taylor series, are described and analysed. The second part of the work deals with the geometric and physical consequences of the first approximation assumption *h/R*<<1. Some versions of the equations describing the state of strain, in particular the tensors of flexible deformation, have been discussed.

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#### References

A. E. LOVE, Mathematical theory of elasticity, Cambridge 1927.

V. Z. VLASOV, General theory of shells and its applications in technology, [in Russian] Gostechizdat, 1949.

N. A. KILCHEVSKY, Generalization of the modern theory of shells, [in Russian] PMM, 4, 2, 1939.

N. A. KILCHEVSKY, Foundations of the analytical mechanics of shells, [in Russian], Kiev 1963.

A. L. GOLDENVEIZER, Theory of thin elastic shells [in Russian], Nauka, 1976.

V. V. Novozimov, Theory of thin shells [in Russian], Sudpromgiz., 1962.

A. E. GREEN, W. ZERNA, Theoretical elasticity, Oxford 1960.

W. FLUGGE, Shells, statical calculations [in Polish], trans]. from 4th ed. Springer-Verlag, New York Inc. 1967.

W. T. KOITER, A consistent first approximation in the general theory of thin elastic shells, Proc. IUTAM Symposium on the theory of thin elastic shells, 12-33, North Holland Publ. Comp., 1960.

J. L. SANDERS, An improved first-approximation theory for thin shells, NASA Tech. Rept., R-24, 1-11.

B. BUDIANSKY, J. L. SANDERS, On the „best" first-order linear shell theory, Progress in Applied Mechanics, The Prager Anniversary Volume, Macmillan Co., 129-140, 1963.

P. M. NAGHD[, Foundations of elastic shell theory, Progress in Solid Mechanics, V, North Holland Publ. Comp., 1963.

P. M. NAGHDI, A new derivation of the general equations of elastic shells, Int. J. Engng. Sci., 1, 509-522, Pergamon Press 1963.

P. M. NAGHDI, Further results in the derivation of the general equations of elastic shells, Int. J. Engng. Sci., 2, 269-273, Pergamon Press 1964.

Cz. WOŹNIAK, Nonlinear theory of shells [in Polish], PWN, Warsaw 1966.

W. T. KOITER, On the nonlinear theory of thin shells, Proc. Kon. Ned. Ak. Wet., ser. B, 69, 1, 1-54, 1966.

N. A. KILCHEVSKY, Elements of tensor calculus and its applications in mechanics [in Russian], Gostechizdat, 1954.

J. L. ERICKSEN, Tensor fields, Handbuch der Physik, III/1, Springer-Verlag, 794, 1964.

E. REISSNER, A new derivation of the equations for the deformations of elastic shells, Amer. J. Math., 63, 177, 1941.