shakedown and limit analysis of 90° pipe bends under internal pressure, cyclic in-plane bending and cyclic thermal loading

the linear matching method is used to create the shakedown limit and limit load interaction curves of 90° pipe bends for a range of bend factors. two load cases are considered i) internal pressure and in-plane bending (which includes opening, closing and reversed bending) and ii) internal pressure and a cyclic through wall temperature difference giving rise to thermal stresses. the effects of the ratios of bend radius to pipe mean radius (r/r) and mean radius to wall thickness (r/t) on the limit load and shakedown behaviour are presented.