Session: DA-01-02 Design and Analysis of Pressure Vessels and Components-2

Paper Number: 123399

123399 - Analytical and Numerical Solutions for the Elastoplastic Buckling Analysis of Shells of Revolution 

The buckling phenomenon is one of the main failure modes encountered in pressure vessels, due to the thin (shell-like) geometry of the structures involved and the predominant compressive stresses frequently observed under standard loads such as external pressure. At present, a few design methodologies exist for these structures with regard to buckling, set out in standard codes such as the ASME Boiler and Pressure Vessel Code (BPVC) or the French CODAP. These rules are either analytical (based on abacuses or empirical formulas) but limited in terms of field of validity, or take the form of recommendations for carrying out finite element analyses in the presence of geometric and/or material non-linearities and possible imperfections.

In this framework, this study aims at providing new efficient solutions for the buckling analysis of most usual components of pressure vessels. Several shells of revolution are considered, such as cylindrical, spherical, ellipsoidal or even conical shells. Various loading cases are explored, among which external pressure plays a prominent role, to which axial compression is added so as to take into account the pressure end thrust effect in pressure equipments. Other combinations of loadings are also investigated. First, some analytical solutions are derived for the elastic/plastic critical buckling loads of perfect shells. While many results are already available in the literature for the elastic case, plastic buckling expressions are mostly original. All the present solutions, whether exact or approximate, must be sufficiently simple (in closed form) and accurate for an efficient and reliable use. They are validated against numerical results from finite element computations performed on a commercial code.

In addition, a numerical tool is developed so as to deal with the post-buckling response of the shells, and particularly with the imperfection sensitivity, which is tricky to solve from an analytical point of view. Arc-length and branch-switching methods are included in the program so as to deal with limit points but also bifurcation points along the incremental force-displacement curves. It allows one to describe all trivial and primary (and even secondary or further) post-critical response branches without the use of any initial imperfection, what serves as a reference for further calculations with initial geometric imperfections. Finally, owing to the periodicity of the buckling modes, use will be made of the analytical solutions (especially the wave numbers of the modal deformed shapes) in order to reduce the numerical models down to a specific unit cell, by using periodic or Bloch-periodic boundary conditions.

 

Keywords: Shells of revolution, buckling, elastoplasticity, external pressure, analytical modeling, finite element formulation, pressure equipments, pressure vessels.

Presenting Author: Gwladys BELONE ENSTA Bretagne

Presenting Author Biography: I'm a PhD student at ensta bretagne, developing simplified analytical solutions for pressure vessels.
My thesis is part of a collaboration with CETIM (Senlis) to contribute to the current CODAP regulations (French dimensioning code).

Authors:

Gwladys BELONE ENSTA Bretagne
Philippe Le Grognec ENSTA Bretagne
Samir Assaf CETIM Centre Technique des Industries Mécaniques
Philippe Rohart CETIM Centre Technique des Industries Mécaniques