(A) study on localized mortar-based gap element method for treating non-matching discrete interfaces

Abstract

A virtual gap element method for treating non-matching interfaces is proposed. The present approach considers the interface treatment of partitioned systems. In a partitioned analysis, a large system is partitioned into several subsystems. Each subsystem is independently discretized with different sizes of finite elements to improve efficiency. When reassembling the partitioned system, non-matching interfaces appear between the substructures. In the case of the curved non-matching interfaces, the finite element model contains void areas along the common interfaces. These voids interfere with the accurate enforcement of interface constraints. In this research, a family of gap elements is introduced in the mortar method to deal with the voids properly. The proposed gap elements have zero strain constraints to obtain accurate interface forces at the non-matched interface nodes. In contrast to the conventional mortar method with classical Lagrange multipliers, the present method can handle interface constraints without complicated surface projection procedures for two- and three-dimensional interface problems. From these characteristics, the gap element method improves the accuracy and efficiency. Furthermore, the proposed method provides better conservation properties, as verified by several numerical examples.