## 1 Introduction  
As an engineering structure becomes more complex, the costs for structural dynamic analysis increase enormously. The computationally intensive design process of large-scale spacecraft needs repetitive calculations with efficient analysis techniques that provide reliable dynamic predictions. Until now, one essential tool for engineers to solve these issues has been dynamic substructuring (DS) technology. Generally, DS methods can be categorized as the component mode synthesis (CMS) method [1; 2], the frequency-based substructuring (FBS) method [3], and the impulse-based substructuring (IBS) method [4]. An overview of DS methods is provided in ref. [5]. The CMS method and the FBS method are two widely used techniques in many industrial fields, and they are relatively well-developed. However, when facing transient impact problems, such as the soft landing process of spacecraft, the CMS and FBS expose shortcomings: a large frequency band should be considered, which makes the analysis expensive and difficult to apply. The IBS method shows an advantage in dealing with transient impact problems [4; 5; 6]. [PERSON] [7] proposed the idea of assembling substructures using impulse response functions (IRFs) of substructures early in 1995. Subsequently, [PERSON] proposed a dual assembly of substructures, named IBS [8], in 2010. This dual form of IBS is easy to implement, and the method is achieved by using either numerical IRFs or measured IRFs [9]. The IBS method expanded the DS techniques in the time domain and was developed by following studies. [PERSON] and [PERSON] [6] proposed a truncation and windowing procedure to limit the cost involved by the discretized convolution product inherent in the IBS method. [PERSON] [10] and [PERSON] used a modal projection to filter the low-frequency contributions from the IRFs, which decreased the required length of the convolution integral. [PERSON] [11; 12] and [PERSON] extended this method by allowing the assembly of structures that are composed of both substructure finite element (FE) models and substructure IRFs. [PERSON] and [PERSON] [13] proposed a rigid-elastic hybrid joint description method that takes the effect of both rigid and elastic connections between substructure IRFs into consideration. [PERSON] and [PERSON] [14] further studied the damping and nonlinearity of joints between substructure IRFs and put the method into practice through the dynamic prediction of the landing progress of a lunar lander. [PERSON] [15] proposed a method for the assembly of multi-domain substructures with general joints. However, when IRFs are generated from an experiment, the support points on the interfaces of each substructure may be mismatched. Furthermore, the FE models usually have non-matching interfaces when two substructures are constructed independently by different design groups. The assembly of IRFs obtained from these FE models has to face difficulties in satisfying compatibility on non-matching interfaces. Historically, there have been three classes of methods for coupling FE models with non-matching interfaces. One class of methods for coupling the independently established FE models with non-matching interfaces is the Lagrange multiplier method. [PERSON] [16; 17] presented hybrid variational formulations for the coupling through an interface and introduced the independent Lagrange multipliers as the tractions on the interface. The equations of the coupled system are obtained by using the principle of minimum potential energy. [PERSON] [18] formed the general-purpose finite element code using hybrid variational formulations. [PERSON] and [PERSON] [19] treated the interface with a displacement frame and a localized version of the method of Lagrange multipliers, and both static and dynamic partitioned structural systems were considered. It is noteworthy that the IBS method is also based on the formulations of the classical Lagrange multipliers.