Investigation on the performance of the expansion water seal by using isogeometric analysis with variational inequalities for the frictional contact

Abstract

In this study, IGA is introduced into the performance analysis of the expansion water seal for an exact representation of its complex geometrical shape. Firstly, the incremental equilibrium equations used in the large deformation analysis are derived for the IGA discretization model based on the updated Lagrangian formulation. The unknown contact forces are directly involved in the equilibrium equations, which results in a simple expression. Then, through the investigation of the contact conditions, the normal and tangential contact forces are verified to be the solutions of two box-constrained variational inequalities representing the normal and tangential contact conditions, respectively. Furthermore, the incremental equilibrium equations for all components of the water seal system and the variational inequalities for all contacts between the components are assembled together and reformulated as a global variational inequality, which is resolved by using the Extra-gradient method. Ultimately, the new method is applied in the performance comparison of two optional expansion water seals, in which the capability and precision of the proposed method are investigated. Results verify that the proposed method is effective in the numerical simulation of the expansion water seal and has a higher precision than the traditional FEM under the same conditions.