Energy-Conserving Variable-Node Interface Elements for Interaction Analysis

Abstract

A new algorithm is proposed to achieve the energy conservation of discrete systems with non-matching interfaces. In a variable-node construction of nonmatching interfaces, additional interface degrees of freedom often need to be created, which means that each time additional interface nodes are added, the system becomes essentially a different discrete system. This is because, even though the resulting discrete system may vary from time to time, its continuum counterpart should remain the same throughout the analysis. The present paper presents an energy conserving strategy when the system nodes vary for each of the partitions. This has been realized by requiring that both the kinetic and strain energy of the new system at the start of the next step should be the same as the final condition of the preceding discrete system. The present energy-conserving strategy is demonstrated via several examples including linear dynamic and FSI problems using smoothed finite element method, which provides a convenient framework for transforming nonmatching meshes into matching mesh by introducing variable-node elements.