Elastic response of a cylinder containing longitudinal stiffeners

This paper develops a three-dimensional analytical model of a cylinder that contains a longitudinal stiffener. The model begins with the equations of motion for a fully elastic solid that produces displacement fields with unknown wave propagation coefficients. These are inserted into stress and displacement equations at the cylinder boundaries and at the location of the stiffener. Orthogonalization of these equations produces an infinite number of indexed algebraic equations that can be truncated and incorporated into a global matrix equation. Solving this equation yields the solution to the wave propagation coefficients and allows the system's displacements and stresses to be calculated. The model is verified by comparison of the results of a plane strain analysis example to a solution generated using finite element theory. A three-dimensional example problem is formulated and the displacement results are illustrated. The inclusion of multiple stiffeners is discussed.

► Analytical model of the displacement of a thick cylinder, which has longitudinal stiffeners embedded in the cylinder wall, is derived. ► Three-dimensional elasticity equations in radial coordinates are mated with the equations of motion of a bar. ► The effects of the cylindrical modes interacting with the stiffener are illustrated. ► A three-dimensional example with a single stiffener is modeled and discussed.