Three dimensional buckling beam under cylindrical constraint.

Highlights • Three dimensional deformation shapes of compressed beam in circular constraints. • Four deformation modes as axial displacement increases. • Critical axial displacement between deformation modes. • Geometrical parameters influence the mode transition. Abstract This paper studies the three dimensional buckling and post buckling process of compressive long elastic beam confined by cylindrical lateral constraint without friction. Based on theoretical analysis and numerical simulations, four stages are identified and characterized as the compressive axial displacement increases from zero: initial two dimensional shape, small three dimensional shape, three dimensional helix shape and three dimensional alpha shape. Critical axial displacement at the transition points between four deformation shapes are studied, and the effect of geometrical parameters such as beam length and constraint size on critical displacement are examined. Special emphasis is paid to identify the transition points from three dimensional helix shape to three dimensional alpha shape, and the transition can be divided into jump regime (sharp transition) and no-jump regime (smooth transition) based on the criterion whether number of helical periods is larger or smaller than one. At the same time, critical number of helical periods in three dimensional helix shape is linearly correlated with a nondimensional geometrical parameter. Graphic abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]