The Estimation of Contact Pressure in Expanded Tube Joints Using Virtual Finite Elements

Abstract

The quality and security of expanded joints depends very much on the details of contact stresses at the interface between the tubes and the tube sheet. The contact problem is one which is severely nonlinear. A new finite element method has been devised that relieves many of the classical difficulties that are often encountered. On the contact surfaces of the tube and the tube sheet are defined meshes of virtual elements. The ephemeral meshes are recreated in each iteration so that their geometry always reflects the most recent configuration of the mesh on the opposite side of the contact interface. All corrective force increments for contact compatibility and equilibrium are calculated by transferring the related quantities to the virtual meshes. On these meshes nodal quantities are re-distributed and re-integrated so that appropriate nodal forms are available for direct comparison. The corrective nodal force vectors for compatibility and equilibrium are designed in such a way that they are optimized to the first order without interfering with each other.