Modeling of viscoelastoplastic deformation of flexible shallow shells with spatial-reinforcements structures

Abstract

Based on the procedure of time steps, a mathematical model of the viscoelastoplastic behavior of shallow shells with spatial reinforcement structures is constructed. Plastic deformation of the components of the composition is described by flow theory with isotropic hardening; viscoelastic deformation by the equations of the Maxwell–Boltzmann model. The possible weakened resistance of composite curved panels to transverse shear is taken into account in the framework of the hypotheses of Reddy's theory, and the geometric nonlinearity of the problem is taken into account in the Karman approximation. The solution of the formulated initial-boundary value problem is constructed using an explicit numerical scheme of the “cross” type. The elastoplastic and viscoelastoplastic flexural dynamic behavior of “flat” and spatially reinforced fiberglass cylindrical panels under the action of explosive loads has been investigated. Using the example of relatively thin composite structures, it is shown that, depending on which of the front surface (convex or concave), a load is applied, replacing the traditional “flat” reinforcement structure with a spatial one can lead to both an increase and a decrease in the residual deflection. However, in both cases, such a replacement can significantly reduce the intensity of residual deformations of the binder material and fibers of some families. It was demonstrated that the amplitudes of oscillations of curved composite panels in the neighborhood of the initial moment of time significantly exceed the maximum absolute values of the residual deflections. In this case, the residual deflections are rather complicated. It is shown that the calculations carried out within the framework of the elastoplastic deformation theory of the composition components do not even allow an approximate the magnitude determination of the residual deformations of the materials making up the composition.

Keywords

• shallow shells
• “flat” reinforcement
• spatial reinforcement
• dynamic deformation
• viscoelastoplastic deformation
• reddy's theory
• maxwell–boltzmann model
• “cross” type scheme