Finite difference model for the buckling analysis of sandwich pipes under external pressure

Abstract

A general eigenvalue buckling solution is developed for the buckling analysis of sandwich pipes with thick cores subjected to internal and external hydrostatic pressure. The formulation accounts for shear deformation effects and involves two destabilizing terms: one is due to the external hydrostatic pressure and incorporates the follower effects, and the other, is due to the pre-buckling stresses undergoing the nonlinear components of strains. Work conjugate triplets consisting the Cauchy stress tensor, the Green-Lagrange strain tensor, and constant constitutive relations are adopted in the formulation. The principle of stationary potential energy is used to formulate the conditions of equilibrium and neutral stability conditions using polar coordinates. A finite difference solution is developed and implemented in MATLAB and then applied to predict the buckling capacity of sandwich pipes consisting of two steel pipes with a soft core. A comprehensive verification study is conducted, and the validity of the formulation is established through comparison with other solutions. A parametric study is then carried out to investigate the effect of internal pressure, the thickness and material properties of the core, internal and external pipe thicknesses, on the buckling of sandwich pipes. Simple design equations are developed to predict the critical pressure of sandwich pipes.