On Spectral Approximation of Static And Dynamical Problems For Elastic Multistructures

The present paper is devoted to the construction and investigation of algorithms of spectral approximation of three-dimensional problems for nonhomogeneous anisotropic elastic multistructures in curvilinear coordinates, which are junctions of three-dimensional body, shell clamped in it and curvilinear rod clamped in shell. Sequences of boundary and initial-boundary value problems defined on the union of three, two and one-dimensional space domains are obtained and investigated in suitable Sobolev spaces. Moreover, the convergence of the sequence of vector-functions of three space variables restored from the solutions of the reduced problems to the solutions of the original three-dimensional problems in corresponding spaces is proved and under additional conditions, the rate of approximation is estimated. Key-Words: Elastic multistructures, spectral approximation, error bounds