Asymptotic theory of the hyperbolic boundary layer in shells of revolution at shock edge loading of the tangential type

Abstract

The present work is devoted to the construction of asymptotically optimized equations of the hyperbolic boundary layer in thin shells of revolution in the vicinity of the dilation wave front at shock edge loading of the tangential type. These equations are derived by asymptotically integrating  of the exact three-dimensional theory elasticity equations in the special coordinate system. This system defines the boundary layer region. The wave front has a complicated form, dependent on the shell curvature and therefore its asymptotical model is constructed. This geometrical model of the front defines it via the turned normals to the middle surface. Also, these turned normals define the geometry of the hyperbolic boundary layer applicability region. Constructed asymptotically optimised equations are formulated for the asymptotically main components of the stress-strain state: the longitudinal displacement and the normal stresses. The governing equation for the longitudinal displacement is the hyperbolic equation of the second order with the variable coefficients. The asymptotically main part of this equation is defined as the hyperbolic boundary layer in plates.

Keywords

• asymptotical theory
• hyperbolic boundary layer
• shock loading of the tangential type
• dilatation wave
• shell of revolution
• transient waves