A Dynamic Shell Theory Coupling Thickness Stress Wave Effects With Gross Structural Response

Abstract

A theory for thick cylindrical shells is presented that couples the early time thickness stress wave propagation with higher-order shell theory equations. The formulation completely describes the continuum response in the thickness direction for “early time” considerations while representing the circumferential response with a high-order circumferential displacement assumption. Late time (structural response) equations are developed to continue the analysis after thickness effects are no longer important. The finite-element method is used to obtain solutions of the theory. Calculations are presented which show that thickness stress need not be included for cylindrical shells with h/R ratios less than 0.2.