Instability of the printing jet during the three-dimensional-printing process

Euler’s instability criterion is widely used in engineering to design a column. However, this criterion is not suitable for judging the instability of a three-dimensional printing process because the axial motion of the printing jet has to be considered. A variational principle is established, and an equivalent Eulerian load is obtained. The theoretical results show that a higher printing velocity makes the moving jet much more stable, and an experiment is designed to verify our theoretical prediction.