A model of a thick-walled anisotropic shell is constructed based on the variational approach. The existence of both kinetic and potential energy is postulated for a shell as for a three-dimensional anisotropic elastic body, and the energy scalar product is defined. Fourier coefficients of the translation vector in the functional basis generated by Legendre polynomials are used as field variables of a continuum system. Using the potential and kinetic energy formulated in terms of field variables the equations of motion and its boundary conditions are derived. These equations have the form of a Lagrange system of the second kind for continua, written in terms of generalized forces that are stress tensor moments in the functional basis implemented. The proposed approximate model of a thick shell is formulated as a N-th-order shell theory.
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