of straight line P_o and s _o^r -P_o¹ . Then the solution of the inverse problem is unique.

Theorem 2. Let W _1, W ₂ be piece-wise smooth, simply-connected bounded domains in R², W = W ₁ È W ₂ . Let us assume, that on ¶ W there exists the point of intersection of the curves ¶ W ₁ and ¶ W ₂. Then the solution of the inverse problem is unique.

ON A METHOD OF CONSTRUCTION OF A

GEOMETRICAL NONLINEAR THEORY OF NON-SHALLOW SHELLS

In the present paper the three-dimensional problems of the geometrical nonlinear theory of elasticity are reduced to the two-dimensional problems of non-shallow shells by means of I. N. Vekua method. Under thin and shallow shells I. Vekua meant elastic bodies of shell type, satisfing the conditions

(1)   a_a ^b - x₃ b_a ^b » a_a ^b _, -h £ x₃ £ h, (a , b = 1, 2),

where aa b , ba b are mixed components of the metric tensor and tensor of the curveture of the shell middle surface, x₃ is a thickness coordinate, h is a semi-thickness, x₁, x₂ are curvilinear coordinates of the middle surface.

In our constructions under non-shallow shells we will mean elastic bodies, free from the assumption of the form (1), i. e, in general,

a_a ^b - x₃ b_a ^b ¹ a_a ^b , but always | x₃ b_a ^b |<1.

There is considered the case, when Hook's law for anisotropic bodies has the following form

s ^ij = E^ijpqe _pq,

where s ^ij are contravariant components of the stress tensor, E^ijpq and e _pq are contravariant and covariant components of the tensors of elasticity and strain, respectively:

E^ijpq = _klmn,

e pq=

here R_i and Rⁱ are co- and contravariant base vectors of the space, U is a vector of desplacement, and _klmn are base vectors and elastic constants in the rectangular system