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Implicit-explicit (IMEX) time integration schemes are well suited for non-linear structural dynamics because of their low computational cost and high accuracy. However, the stability of IMEX schemes cannot be guaranteed for general non-linear problems. In this article, we present a scalar auxiliary variable (SAV) stabilization of high-order IMEX time integration schemes that leads to unconditional stability. The proposed IMEX-BDFk-SAV schemes treat linear terms implicitly using kth-order backward difference formulas (BDFk) and non-linear terms explicitly. This eliminates the need for iterations in non-linear problems and leads to low computational costs. Truncation error analysis of the proposed IMEX-BDFk-SAV schemes confirms that up to kth-order accuracy can be achieved and this is verified through a series of convergence tests. Unlike existing SAV schemes for first-order ordinary differential equations (ODEs), we introduce a novel SAV for the proposed schemes that allows direct solution of the second-order ODEs without transforming them into a system of first-order ODEs. Finally, we demonstrate the performance of the proposed schemes by solving several non-linear problems in structural dynamics and show that the proposed schemes can achieve high accuracy at a low computational cost while maintaining unconditional stability. 

Simulating the dynamics of structural systems containing both stiff and flexible parts with a time integration scheme that uses a uniform time-step for the entire system is challenging because of the presence of multiple spatial and temporal scales in the response. We present, for the first time, a multi-time-step (MTS) coupling method for composite time integration schemes that is well-suited for such stiff-flexible systems. Using this method, the problem domain is divided into smaller subdomains that are integrated using different time-step sizes and/or different composite time integration schemes to achieve high accuracy at a low computational cost. In contrast to conventional MTS methods for single-step schemes, a key challenge with coupling composite schemes is that multiple constraint conditions are needed to enforce continuity of the solution across subdomains. We develop the constraints necessary for achieving unconditionally stable coupling of the composite ρ∞-Bathe schemes and prove this property analytically. Further, we conduct a local truncation error analysis and study the period elongation and amplitude decay characteristics of the proposed method. Lastly, we demonstrate the performance of the method for linear and nonlinear stiff-flexible systems to show that the proposed MTS method can achieve higher accuracy than existing methods for time integration, for the same computational cost. 

Multi-axial real-time hybrid simulation (maRTHS) uses multiple hydraulic actuators to apply loads and deform experimental substructures, enacting bothtranslationalandrotationalmotion. This allows for an increased level of realism in seismic testing. However, this also demands the implementation of multiple-input, multiple-output control strategies with complex nonlinear behaviors. To realize true real-time hybrid simulation at the necessary sub-millisecond timescales, computational platforms will need to support these complexities at scale, while still providing deadline assurance. This paper presents initial work towards supporting (and is influenced by the need for) envisioned larger-scale future experiments based on the current maRTHS benchmark: it discusses aspects of hardware, operating system kernels, runtime middleware, and scheduling theory that may be leveraged or developed to meet those goals. This work aims to create new concurrency platforms capable of managing task scheduling and adaptive event handling for computationally intensive numerical simulation and control models like those for the maRTHS benchmark problem. These should support real-time behavior at millisecond timescales, even for large complex structures with thousands of degrees of freedom. Temporal guarantees should be maintained across behavioral and computational mode changes, e.g., linear to nonlinear control. Pursuant to this goal, preliminary scalability analysis is conducted towards designing future maRTHS experiments. The results demonstrate that the increased capabilities of modern hardware architectures are able to handle larger finite element models compared to prior work, while imposing the same latency constraints. However, the results also illustrate a subtle challenge: with larger numbers of CPU cores, thread coordination incurs more overhead. These results provide insight into the computational requirements to support envisioned future experiments that will take the maRTHS benchmark problem to nine stories and beyond in scale. In particular, this paper (1) re-evaluates scalability of prior work on current platform hardware, and (2) assesses the resource demands of a basic smaller scale model from which to gauge the projected scalability of the new maRTHS benchmark as ever larger and more complex models are integrated within it.