INVESTIGATING THE DYNAMIC BEHAVIOR OF A THICK SPHERE STRESS STATE UNDER A MOBILE LOADING ON AN EXTERNAL BOUNDARY

T. I. Zmushko, Yu. N. Bukharev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1984. Вып.3. С. 49-53.

      A method of space characteristics is used to study elastic wave propagation and forming the highest stress regions (that is maximum stress rate regions) for a thick sphere which experiences dynamic load on its external surface h = 0,5R, h is the shell thickness, R is the external radius). Die external load is assumed to be determined by two stress tensor components (σ_rr normal and τ_kθ tangent) and its application region varies with time. The sphere being studied occupies the R^l≤r≤R, region within the r, θ, φ spherical coordinates, where 0≤θ≤π/2, is uniform, isotropic, and has linearly elastic properties defined by the density, ρ, longitudinal wave velocity, α, and transverse wave velocity, β. Axial symmetry requirements are assumed to be met.