On elasticity relationships in the linear theory of thin elastic shells: PMM vol. 34, n≗6, 1970, pp. 1136–1138

Abstract

Questions of constructing tensor elsticity relationship within the accuracy of the Kirchhoff-Love hypothesis are discussed herein. It is clarified that it is impossible to conserve simultaneously the static-geometric analogy and to assure applications of theorems of the theory of elasticity by using not too complex elasticity relationships. In this connection, two modifications of the elasticity relationships in the linear theory of thin elastic shells are proposed. The second modification retains these theorems in the linear theory of thin elastic shells. The second modification satisfies the requirements of the static-geometric analogy, but violates the reciprocity theorems (in the small). Among the possible modifications of the elasticity relationships used in the linear theory of thin elastic shells, one of the most simple ones is the modification presented by the authors of [1] and [2]. Nevertheless, these relationships answer a number of requirements to be discussed below. At the same time authors of [3] indicated that these relationships are not tensor character. In this paper we consider the construction of tensor elasticity relationships differing slightly in the lines of curvature from relationships presented in [1] and [2].