Combined Mortar Finite Element Method Using Dual Lagrange Multiplier and BDD-MPC Method for Large-scale Assembly Structures

A numerical method is proposed in the present paper for structural analysis of large-scale assembly structures. The mortar finite element method (FEM) has been developed for assembling structural components modeled by finite elements and a set of constraints in a weak form, which is formulated using Lagrange multipliers. In the dual Lagrange multiplier method proposed by Wohlmuth, a set of biorthogonal shape functions is used to discretize Lagrange multipliers. One of the present authors proposed a method to incorporate multi-point constraints (MPCs) into the balancing domain decomposition (BDD) method, which was proposed by Mandel. The method, which is called the BDD-MPC method in this paper, can solve large-scale structural problems having many MPCs at high speed using parallel computers. The proposed method for large-scale assembly structures combines the above two methods, i.e., the mortar FEM using the dual Lagrange multipliers and the BDD-MPC method. A numerical integration method using back ground cells for integrating the constraints in a weak form is also proposed. In this method, square and fine integration cells are arranged as a grid without considering the shapes of surface elements on the surfaces to be connected. The integration method is verified by investigating the levels of details of divisions of both meshes to be connected and the integration cells. In the illustrative example of two cubes that are connected by the dual Lagrange multipliers, very fine mesh division is necessary to obtain a solution with sufficient accuracy. It is demonstrated that the BDD-MPC method is a powerful tool to solve such a problem. Computation performances of the method are also investigated. © 2023 by the Japan Society for Computational Engineering and Science.