Despite advancements in experimental and numerical techniques (high-performance testing and powerful FEA software), assessing large-scale, complex structural systems remains challenging. Difficulties arise from the complexities inherent in these systems, including: * Large dimensions (nuclear power plants, offshore structures, dams, etc.). * Varied materials and structural components (concrete, steel, masonry, beams, columns, etc.). * Complex loading scenarios (static, seismic, impact, thermal, wind, etc.). * Multiple physical fields and interactions (fluids, structures, soils, etc.). Conventional methods often involve scaled physical tests or simplified numerical models due to the computational limitations of comprehensively modeling all aspects. Integrated simulation methods (partitioned or coupled methods) offer a solution by decomposing large problems into smaller, manageable ones. This is particularly beneficial in academic settings where specialized methods often lack reusability. This approach enables different analysis programs, such as VecTor (specialized for reinforced concrete) to be used with others like Abaqus or OpenSees (for soil-structure interaction), for example. The system's equation of motion (Ma + Cv + R = F) can be decomposed into substructures at the component level (focusing on damping and restoring forces) or the system level (decomposing mass, damping, and restoring forces). This research focuses on system-level decomposition, involving the coupling of dynamic subsystems. The paper focuses on the development of a new staggered system-level decomposition method.

The authors review monolithic and partitioned approaches to solving coupled problems. Monolithic methods treat the entire system as a single entity, solving all components simultaneously. While efficient for direct interaction, they are difficult to implement. Partitioned methods, conversely, treat subsystems as separate entities stepped in time, allowing different time integration schemes. Interaction is managed iteratively, passing variables between subsystems until convergence. Partitioned methods are favored for easier implementation, especially when using existing FE programs, but staggered and iterative approaches both have limitations. Staggered methods, while simpler for code reuse, are approximate and only conditionally stable. Iterative methods improve accuracy and stability but are difficult to implement in multiple programs due to the requirement for rollback capabilities within the software, which many FEA packages lack.

The authors propose a new staggered method to directly integrate dynamic substructures modeled using different analysis programs. This method aims for straightforward implementation by only exchanging data through standard input/output. Each program is treated as a black box, requiring only the ability to impose predicted displacements at interface DOFs and retrieve reaction forces. The method is detailed using a three-DOF mass-spring-damper system, decomposed into two substructures (Sub-i and Sub-j). Numerical time integration (predictor-corrector) is applied. Two coupling methods are proposed. Method 1 assumes displacement, velocity, and acceleration continuity at the interface. Method 2, directly uses predictors for displacement and velocity to determine the interaction force. A staggered algorithm is outlined, where the substructures are integrated alternatively, passing interaction terms (Aij and Dij,n+1). A parametric study compares the two methods using Newmark's average acceleration method (NAA) and the explicit Newmark method (ENM), with variations in mass and stiffness ratios between substructures. The influence of different integration schemes (NAA, ENM) on accuracy and stability is assessed. The stability is mathematically evaluated using the energy method (for mixed schemes). For α-modified integration schemes (to filter high frequencies), a more general stability analysis method is proposed using "stability counterparts" for primary and secondary substructures; this involves determining the maximum allowable time step for each substructure, and the integrated simulation must use a step less than the minimum of these.

The parametric study revealed that Method 2 (directly using predictors for interaction force) is more accurate than Method 1 but less stable. Method 2 is only conditionally stable, even with unconditionally stable schemes in both substructures. The stability analysis, using the energy method for Newmark schemes and a general method for α-modified schemes, provides a practical way to determine maximum stable time steps. The general stability analysis method considers stability counterparts for each substructure, conservatively estimating the critical time step for the integrated simulation. For unconditionally stable integration schemes, stability depends solely on the positive definiteness of the equivalent interface mass matrix. The analysis of the five-story building example verified the method's applicability to nonlinear problems and confirmed the accuracy of the proposed stability method. The soil-structure interaction analysis of the gravity dam demonstrated the method's capability for large-scale systems, showing good agreement between the integrated and standalone models.

The proposed method successfully addresses the challenges of integrating dynamic substructures modeled with different analysis programs. The focus on using standard input/output for data exchange promotes code reuse and simplifies implementation. The provided stability analysis is crucial for ensuring reliable results and offers a practical approach that accommodates varied integration schemes. The method's accuracy and stability are demonstrated through rigorous numerical examples, showcasing its potential for analyzing complex, large-scale systems. The findings contribute to the development of more efficient and flexible simulation frameworks.

This paper presents a novel staggered method for integrating dynamic substructures modeled using different analysis programs. The method's key strength lies in its simple implementation and ability to use various time integration schemes. A practical stability analysis method is developed and verified through numerical examples, demonstrating the method's accuracy and potential for large-scale, complex systems. Future work will focus on relaxing the linear-elastic assumption for interface layers to allow for even larger time steps.

The study primarily focuses on algorithm development and verification. The examples chosen are illustrative; more extensive testing across a broader range of system types and complexities would strengthen the conclusions. The linear-elastic assumption for the primary substructure (interface layers) can limit the maximum stable time step; future research aims to relax this assumption.