Abstract
The application of shifted Chebyshev polynomials of the second kind to the construction of the thin-body theory is considered. Some basic and additional recurrence relations for Chebyshev polynomials are given. Arbitrary-order moments are obtained for the first and second derivatives of a tensor field and for some expressions. Several equations of motion expressed in terms of the moments of displacement and rotation vectors are derived for the moment theory; a number of constitutive relations of the zeroth approximation are obtained.
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