REFINED MODEL OF VISCO-ELASTIC-PLASTIC DEFORMATION OF REINFORCED FLEXIBLE SHALLOW SHELLS

The initial-boundary value problem of the visco-elastic-plastic behavior of flexible shallow shells reinforced along parallel surfaces is formulated. The inelastic behavior of the materials of the components of the composition is described by the equations of the theory of plastic flow with isotropic hardening. Viscoelastic deformation is determined by the relations of the Maxwell -Boltzmann model. Geometric nonlinearity is taken into account in the Karman approximation. The obtained resolving equations and boundary conditions allow with varying degrees of accuracy to determine the stress-strain state (including the residual state) in the components of the composition of curved panels. The low resistance of the reinforced structure to transverse shear is taken into account. In the first approximation, the equations and boundary conditions corresponding to the traditional non-classical Reddy theory follow from the relations obtained. The numerical solution of the formulated initial-boundary value problem is based on an explicit “cross” scheme. The features of visco-elastic-plastic dynamic deformation of an orthogonal reinforced cylindrical rectangular panel under the action of a load caused by an air blast wave are investigated. It is shown that in some cases even for relatively thin reinforced shallow shells, Reddy's theory is unacceptable for obtaining adequate results of calculations of their visco-elastic-plastic dynamic behavior. It has been demonstrated that the shape and size of the residual deflections of curved composite panels substantially depend on which face surface of the structure (convex or concave) an external load is applied. It was found that in both cases of loading, residual deflections lead to the formation of longitudinal folds in a thin cylindrical reinforced panel.