An explicit time-marching procedure for elastodynamic analyses based on adaptive time-integration parameters and time-step values

Abstract

This study discusses an explicit time-marching procedure that is designed for the time-domain resolution of elastodynamic models considering their physical properties and adopted spatial discretizations. The technique is entirely automated and proves itself to be highly effective, featuring second-order accuracy, adaptive algorithmic dissipation and extended stability limits. Additionally, the discussed methodology is truly explicit, truly selfstarting, and it incorporates automated subdomain/sub-cycling splitting procedures to enhance its overall performance. Thus, the algorithm automatically divides the domain of the problem into different subdomains, adjusting their time-step values according to the properties of the discretized model, which allows improving the efficiency and the accuracy of the analysis, while ensuring stability. Locally-defined adaptive time-integration parameters are also considered, establishing an entirely self-adjustable formulation. In this case, expressions for the timeintegration parameters are provided based on the local features of the discrete model, allowing to create a further link between the adopted temporal and spatial discretization procedures, better counterbalancing their errors. These parameters are locally formulated to nullify the bifurcation spectral radius of the method at pre-established sampling frequencies, providing maximal numerical damping at the highest sampling frequency of the elements of the adopted spatial discretization. This design optimizes the formulation to mitigate the influence of spurious high-frequency modes on the computed responses, allowing for enhanced analyses. In fact, the primary goal of introducing numerical damping is to eliminate non-physical spurious oscillations that may arise from the excitation of spatially unresolved modes. Therefore, the methodology not only tracks down the frequency range of the discretized model, but also it is designed to adaptively enforce significantly low values (close to zero) for the spectral radius of the method at the highest frequencies of the model, as well as it aims to provide relatively high spectral radius values (close to one, considering physically undamped models) in the important low-frequency range. Benchmark analyses are conducted at the end of this study to demonstrate the technique's effectiveness taking into account theoretical problems and complex models that are representative of real-world applications in the OIL & GAS industry.