Buckling finite element formulation for sandwich pipes under external pressure

A finite element buckling eigenvalue solution is developed for the analysis of sandwich pipes subjected to internal and external hydrostatic pressure. The principle of stationary potential energy is used to formulate the conditions of equilibrium and neutral stability using polar coordinates. The formulation accounts for shear deformation effects and is suited for sandwich pipe systems with thick cores. It 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-bucking stresses undergoing nonlinear components of strains. The formulation adopts a work conjugate triplet consisting the Cauchy stress tensor, the Green Lagrange strain tensor, and constant constitutive relations. A finite element solution is developed and implemented under MATLAB and is then applied to predict the buckling capacity of sandwich pipes consisting of two steel pipes with a soft core. A verification study is conducted, and the validity of the formulation is established through comparison with other solutions. A parametric study is then conducted to investigate the effect of hydrostatic internal pressure, core material, core thickness, internal and external pipe thicknesses, on the buckling capacity of sandwich pipes.