Asymptotic Theory of Anisotropic Plates and Shells

On Asymptotic Theory of Beams, Plates and Shells

“…Classic theory of plates does not take into account the boundary layer, which consists of antiplane and plane boundary layers, the parameters of which, when removing from the bank surface inwards the plate, diminish exponentially, but with essentially di erent indexes of the exponent. Asymptotic theory of anisotropic plates and shells is built in [12].…”

“…The solutions of the formulated problems again have the form of (12), and the solution of the outer problem -(18), yet, after the substitution of (18) into system (35) we only get noncontradictory system at…”

“…The iteration cuts o after the rst two step, we have In the monographs [12,14] the solution of nonclassical boundary-value problems set for one-layered and layered anisotropic plates and shells are brought.…”

“…The values q I in each problem are determined only in one way. For our problem we have [12] qσ xx = − , qσ xy = − , qσ yy = , qu = − , qv = − . (19) Substituting (18), (19) into system (17) and having solved once again obtained system, we shall have…”

“…The values of the rst ten roots λn are brought in [12]. From the rst two formulae (28) and conditions (26) very important property in the boundary layer follows-selfbalance of stresses σ xxb and σ xyb in the arbitrary crosssection γ = γ k :…”