Mathematical modeling of the dynamic behavior of structurally nonuniform casings of explosion chambers

Abstract

individual structural nonuniformities and eccentric application of the explosive load were studied. All the designs of structurally nonuniform casings of explosion chambers have been developed on the basis of empirical data, engineering intuition, and full-scale modeling, requiring considerable material expenses. In this paper, we develop an approach to numerical modeling of the dynamics of structurally nonuniform casings of explosion chambers which are shells of revolution fitted with a longitudinal and transverse set of discrete reinforcements, also playing the role of shock wave dampers. This approach will allow us to make recommendations for choosing the parameters of the reinforcing elements for specific explosion chamber designs. 1. Formulation of the Problem. The explosion chamber is a three-walled shell of revolution or a combination of threewalled shell elements of very simple shape. The outer wall of the structure is a continuous shell. A longitudinal and transverse set of T-shaped ribs forms the filler wall and inner wall, which is weakened by holes due to the design of the structure. As the explosion wave arrives at the inner surface, partial breakup and partial reflection of the explosion wave occurs. The rarefaction explosion wave interacts with the internal framework and the external geometric shell and the result is damping of the wave. This design allows us to distribute the explosive load in time and space, making it possible to decrease the stress level on the elements of the explosion chamber. 2. Mathematical Model for the Explosion Chamber. The equations of motion in a Timoshenko type theory of shells and rods form the basis of the mathematical model for a structurally nonuniform structure with discrete filler. The stress-strain state of the engineered structure is determined within the hypotheses of the geometrically nonlinear theory of shells and rods. To derive the equations of motion, we use the Hamiiton-Ostrogradskii nonsteady-state variational principle, according to which