Engineering topics

Brock, Jerry S.

Publications and source records attributed to Brock, Jerry S..

3 records

DOE OSTI2016

Benchmark solution of the dynamic response of a spherical shell at finite strain

Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method by means of numerical examples with finite deformations and material non-linearities and inelasticity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

The dynamic sphere test problem

In this manuscript we define the dynamic sphere problem as a spherical shell composed of a homogeneous, linearly elastic material. The material exhibits either isotropic or transverse isotropic symmetry. When the problem is formulated in material coordinates, the balance of mass equation is satisfied automatically. Also, the material is assumed to be kept at constant temperature, so the only relevant equation is the equation of motion. The shell has inner radius r i and outer radius r o . Initially, the shell is at rest. We assume that the interior of the shell is a void and we apply a time-varying radial stress on the outer surface.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2012

The Jump-Off Velocity of an Impulsively Loaded Spherical Shell

We consider a constant temperature spherical shell of isotropic, homogeneous, linearly elastic material with density ρ and Lamé coefficients λ and μ. The inner and outer radii of the shell are r i and r o , respectively. We assume that the inside of the shell is a void. On the outside of the shell, we apply a uniform, time-varying pressure p(t). We also assume that the shell is initially at rest. We want to compute the jump-off time and velocity of the pressure wave, which are the first time after t = 0 at which the pressure wave from the outer surface reaches the inner surface. This analysis computes the jump-off velocity and time for both compressible and incompressible materials. This differs substantially from [3], where only incompressible materials are considered. We will consider the behavior of an impulsively loaded, exponentially decaying pressure wave p(t) = P 0 e -αt , where α ≥ 0. We notice that a constant pressure wave P(t) = P 0 is a special case (α = 0) of a decaying pressure wave. Both of these boundary conditions are considered in [3].

36 MATERIALS SCIENCE↗