Dynamics of Asymmetric Three-Layer Hemispherical Shells with a Discrete-Inhomogeneous Filler Under Pulsed Loads

The paper deals with the dynamics of asymmetric three-layer hemispherical shells with the discretely symmetric lightweight, rib-reinforced filler under pulsed loads. Since the distances between the ribs are much larger than the dimensions of the rib cross-sections, the theory of independent static and kinematic hypotheses for each layer is applied. In asymmetric shells, the load-bearing layers are made of different materials and have various thicknesses. The equations of motion of asymmetric three-layer spherical shells and natural boundary conditions are obtained using the Hamilton- Ostrogradsky variational principle for the Timoshenko-type shell and rod theory model. This makes it possible to develop an adequate finite element model for asymmetric three-layer shells composed of several materials and obtain numerical results on the dynamic behavior of an asymmetric three-layer elastic structure using the finite element method. The influence of physical and mechanical parameters of asymmetric layers of hemispherical shells on the stress-strain state under axisymmetric internal pulse loading is investigated. New mechanical effects are revealed.