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This paper presents a novel, non-iterative, general formulation for the transient analysis of interacting elastodynamic systems in contact that may exhibit relative motion with respect to each other. The overall system consists of a collection of individual structures (subsystems). Each of the structure is solved at first independently of the others assuming no interactive contact forces exist. The solution of the overall system is obtained by enforcing compatibility of displacements and dynamic force equilibrium at the interface boundaries using dynamic ‘mortar elements’. The proposed method obtains the solution in a time marching fashion without the need for iterations. The proposed coupling algorithm is versatile and is designed to accommodate different numerical time integration schemes and different mathematical model solving techniques. The proposed method is computationally advantageous to the substructure methods reported in the literature, which usually use the iterative procedure. It is also computationally efficient to the methods using the monolithic approach, since smaller systems are solved at a time and there is no need to update structural matrices at every time step. The proposed method is verified through comparisons with results reported in the literature. The verification examples demonstrate the accuracy and the computational efficiency of the proposed algorithm.

A robust non-iterative algorithm for multi-body dynamics and vehicle–structure interaction analysis