Modeling frictional contact in shell structures using variational inequalities

A new variational inequality-based formulation is presented for the large deformation analysis of frictional contact in shell structures. This formulation is based on a seven-parameter continuum shell model which accounts for the normal stress and strain through the shell thickness and accommodates double-sided shell contact. The kinematic contact conditions are expressed accurately in terms of the physical contacting surfaces of the shell. Furthermore, Lagrange multipliers are used to ensure that the kinematic contact constraints are accurately satisfied and that the solution is free from user-defined parameters. Large deformations and rotations are accounted for by invoking the Piola-Kirchhoff stress and the Green-Lagrange strain measures. Three examples involving a strip friction test, ring contact and sheet compression tests are used to verify the developed formulations and algorithms, and test various aspects of the solution technique. Photoelastic analysis of the ring compression example is performed for experimental verification. © 1999 Elsevier Science B.V. All rights reserved.