Structure of rod-shell theories in Hilbert space (Q1201678)

The paper builds theories of rods and shells by means of approximation of three-dimensional equations. We stipulate for every field (such as stress, displacement, etc.) on each cross-section (two-dimensional domain) of rods to belong to weight quadratically integrable function space -- a Hilbert space \(L^ 2\), and on the normal region of shell, too. As a result, we can use some properties of Hilbert space, especially the existence of complete series, for structuring rod-shell theories (finite quantities) and meantime for obtaining error estimate for the system of equations, by means of cutting off the complete series.