Refined Model of the Dynamic Behavior of Flexible Reinforced Shallow Shells Made from Nonlinear Elastic Materials

An initial-boundary-value problem is formulated for the dynamic deformation of flexible reinforced shallow shells made of composite materials whose components are nonlinearly elastic. The geometric nonlinearity is taken into account in the Karman approximation. The resulting equations allow one, with different degrees of accuracy, to determine the strain state of such thin-wall structures with account of their weakened resistance to transverse shears. The relatios of the traditional nonclassical Reddy theory follow from these equations as a special case. Numerical integration of the problem stated is carried out on the basis of the method of steps in time by using an explicit “cross”-type scheme. Thin shallow spherical shells and flexible annular plates are considered. They are reinforced in the radial and circumferential directions, contain an absolutely rigid insert, and are clamped along the outer edge. The dynamic behavior of such structures is studied in relation to the level of pressure caused by the blast of air waves and to the form (convex or concave of the face) to which this pressure is applied. It is revealed that, at time intervals exceeding 0.1 s, mechanical behavior of the reinforced shallow shells and plates calculated by the Reddy theory significantly differs from the dynamic response determined according to the refined theory proposed.