Elasto-plastic finite element analysis of squaring circular tube
(Department of Mechanical and Computer-Aided Engineering, St. John’s University, Taipei 25135, China)
Abstract: The flow rule of Prandtl-Reuss was adopted and incremental elasto-plastic finite-element analysis formulation of Coulomb’s friction law combining the finite deformation theory was established, and Lagrangian formulation for simulating the squaring process of circular tube was updated. Incremental Coulomb’s friction law was used in the global stiffness matrix to solve the sliding-sticking state of friction at the boundary contact interface. During the squaring process, the linear factor rmin was adopted to solve the non-linear boundary problems of changing node contact and separation, elasto-plastic transient situation in an element and the non-linear constitutive behavior of material so as to make each reasonable increment of the punch meet the demand of calculation for linear increment. The squaring process of circular tube, load distribution and final shape of work piece after unloading were simulated by this mode and compared with research data. It is known that the circular tube with higher geometrical ratio (R/t) could be pressed into symmetric square tube without collapse. This result can provide reference for the analysis of this process and evaluation and improvement of product defects.
Key words: elasto-plasticity; finite-element; square tube; collapse