Biorthogonal integral transformations in the problems of structural mechanics of shells

摘要

The paper deals with generalised vector finite integral transformation designed for the solution of initial boundary value problems described by systems of linear differential equations in partial derivatives. Described structural algorithm method provides for the construction of adjoint and invariant operators, that in contrast to the method of eigen function expansion can be considered non- selfadjoint boundary value problems with asymmetric matrix coefficients in the system of equations. An essential feature of the proposed method is the ability to produce all the components of the solution including two vectors of sound functions without any a priori information. The proposed procedure is demonstrated as a new method of analytical solution of the nonstationary problem for a shell of revolution with an arbitrary meridian.